// Numbas version: finer_feedback_settings
{"navigation": {"preventleave": false, "showresultspage": "oncompletion", "allowregen": true, "onleave": {"message": "", "action": "none"}, "reverse": true, "showfrontpage": false, "browse": true}, "showQuestionGroupNames": false, "metadata": {"description": "<p>Some questions which demonstrate the adaptive marking feature.</p>", "licence": "Creative Commons Attribution 4.0 International", "notes": ""}, "allQuestions": true, "percentPass": 0, "name": "e-assessment question demo", "questions": [], "pickQuestions": 0, "timing": {"timedwarning": {"message": "", "action": "none"}, "allowPause": true, "timeout": {"message": "", "action": "none"}}, "feedback": {"allowrevealanswer": true, "showtotalmark": true, "showactualmark": true, "advicethreshold": 0, "showanswerstate": true, "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "never"}, "question_groups": [{"questions": [{"name": "Adaptive marking: quadratic equation", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "variable_groups": [{"name": "Quadratic equation", "variables": ["roots", "a", "b", "xs", "ys"]}], "parts": [{"unitTests": [], "marks": 0, "sortAnswers": true, "variableReplacements": [], "showCorrectAnswer": true, "prompt": "<p>A quadratic function&nbsp;$f(x)$ goes through the points $(\\var{xs[0]},\\var{ys[0]})$,&nbsp;$(\\var{xs[1]},\\var{ys[1]})$ and&nbsp;$(\\var{xs[2]},\\var{ys[2]})$.</p>\n<p>Find the two roots of $f$.</p>\n<p>First root:&nbsp;[[0]]</p>\n<p>Second root:&nbsp;[[1]]</p>", "gaps": [{"maxValue": "a", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "variableReplacements": [], "scripts": {}, "marks": "1", "correctAnswerStyle": "plain", "correctAnswerFraction": false, "showCorrectAnswer": true, "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "allowFractions": false, "customMarkingAlgorithm": "", "minValue": "a", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"maxValue": "b", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "variableReplacements": [], "scripts": {}, "marks": "1", "correctAnswerStyle": "plain", "correctAnswerFraction": false, "showCorrectAnswer": true, "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "allowFractions": false, "customMarkingAlgorithm": "", "minValue": "b", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "type": "gapfill", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"unitTests": [], "marks": 0, "sortAnswers": false, "variableReplacements": [], "showCorrectAnswer": true, "prompt": "<p>Write&nbsp;a quadratic function $g(x)$ whose roots are the values you entered above, with $x^2$ coefficient $1$.</p>\n<p>$g(x) =&nbsp;$&nbsp;[[0]]</p>", "gaps": [{"vsetRange": [0, 1], "unitTests": [], "variableReplacements": [{"part": "p0g0", "variable": "a", "must_go_first": false}, {"part": "p0g1", "variable": "b", "must_go_first": false}], "marks": 1, "checkVariableNames": false, "showPreview": true, "answer": "(x-{a})(x-{b})", "showCorrectAnswer": true, "vsetRangePoints": 5, "expectedVariableNames": [], "failureRate": 1, "checkingAccuracy": 0.001, "type": "jme", "scripts": {}, "checkingType": "absdiff", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "type": "gapfill", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"maxValue": "mean(roots)", "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "correctAnswerFraction": false, "scripts": {}, "marks": 1, "correctAnswerStyle": "plain", "variableReplacements": [{"part": "p0", "variable": "roots", "must_go_first": false}], "showCorrectAnswer": true, "prompt": "<p>What is the midpoint of the two roots of $f$?</p>", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "allowFractions": false, "customMarkingAlgorithm": "", "minValue": "mean(roots)", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "statement": "<p>(This question doesn't make a lot of pedagogic sense, it just shows off how adaptive marking works)</p>", "ungrouped_variables": [], "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "functions": {}, "preamble": {"js": "", "css": ""}, "metadata": {"description": "<p data-bind=\"html: 'hi'\">Give the student three points lying on a quadratic, and ask them to find the roots.</p>\n<p data-bind=\"html: 'hi'\">Then ask them to find the equation of the quadratic, using their roots. Error in calculating the roots is carried forward.</p>\n<p data-bind=\"html: 'hi'\">Finally, ask them to find the midpoint of the roots (just for fun). Error is carried forward again.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "advice": "", "variables": {"roots": {"name": "roots", "description": "", "templateType": "anything", "definition": "sort(shuffle(list(-5..5))[0..2])", "group": "Quadratic equation"}, "b": {"name": "b", "description": "<p>Greatest root of the quadratic</p>", "templateType": "anything", "definition": "roots[1]", "group": "Quadratic equation"}, "xs": {"name": "xs", "description": "<p>Three given x coordinates</p>", "templateType": "anything", "definition": "shuffle(-5..5 except [a,b])[0..3]", "group": "Quadratic equation"}, "a": {"name": "a", "description": "<p>Least root of the quadratic equation</p>", "templateType": "anything", "definition": "roots[0]", "group": "Quadratic equation"}, "ys": {"name": "ys", "description": "<p>y coordinates corresponding to the given x coordinates</p>", "templateType": "anything", "definition": "map((x-a)*(x-b),x,xs)", "group": "Quadratic equation"}}, "rulesets": {}}, {"name": "Adaptive marking: rotation matrix", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "variables": {"rad_rotation": {"name": "rad_rotation", "description": "<p>Angle of rotation in radians</p>", "templateType": "anything", "group": "Rotation matrix", "definition": "radians(rotation)"}, "det_m": {"name": "det_m", "description": "", "templateType": "anything", "group": "Rotation matrix", "definition": "det(mat)"}, "mat": {"name": "mat", "description": "<p>Rotation matrix for the given rotation</p>", "templateType": "anything", "group": "Rotation matrix", "definition": "matrix([\n  [cos(rad_rotation),-sin(rad_rotation)],\n  [sin(rad_rotation),cos(rad_rotation)]\n])"}, "rotation": {"name": "rotation", "description": "<p>Angle of rotation in degrees</p>", "templateType": "anything", "group": "Rotation matrix", "definition": "random(10..90)"}}, "variable_groups": [{"name": "Rotation matrix", "variables": ["rotation", "rad_rotation", "mat", "det_m"]}], "parts": [{"gaps": [{"correctAnswerFractions": false, "numRows": "2", "scripts": {}, "marks": "4", "precisionType": "dp", "precisionPartialCredit": 0, "variableReplacements": [], "showCorrectAnswer": true, "markPerCell": true, "allowResize": false, "type": "matrix", "strictPrecision": false, "allowFractions": false, "correctAnswer": "mat", "precision": "2", "numColumns": "2", "tolerance": 0, "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacementStrategy": "originalfirst"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "type": "gapfill", "prompt": "<p>Write a matrix $\\mathrm{M}$ corresponding to a rotation of $\\var{rotation}^{\\circ}$ anti-clockwise about the origin.</p>\n<p>Round numbers to 2 decimal places.</p>\n<p>$\\mathrm{M} = $&nbsp;[[0]]</p>", "variableReplacementStrategy": "originalfirst"}, {"gaps": [{"maxValue": "det(mat)", "correctAnswerFraction": false, "precision": "2", "showPrecisionHint": false, "marks": 1, "precisionType": "dp", "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [{"part": "p0g0", "variable": "mat"}], "strictPrecision": false, "type": "numberentry", "scripts": {}, "allowFractions": false, "minValue": "det(mat)", "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "type": "gapfill", "prompt": "<p>$\\operatorname{det}\\mathrm{M} = $&nbsp;[[0]] (Round your answer to 2 decimal places)</p>", "variableReplacementStrategy": "originalfirst"}, {"gaps": [{"correctAnswerFractions": false, "numRows": "2", "scripts": {}, "marks": 1, "precisionType": "dp", "precisionPartialCredit": 0, "variableReplacements": [{"part": "p0g0", "variable": "mat"}, {"part": "p1g0", "variable": "det_m"}], "showCorrectAnswer": true, "markPerCell": false, "allowResize": false, "type": "matrix", "strictPrecision": false, "allowFractions": false, "correctAnswer": "matrix([[mat[1][1],-mat[0][1]],[-mat[1][0],mat[0][0]]])/det_m", "precision": "2", "numColumns": "2", "tolerance": 0, "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacementStrategy": "originalfirst"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "type": "gapfill", "prompt": "<p>$\\mathrm{M}^{-1} = $&nbsp;[[0]]</p>\n<p></p>", "variableReplacementStrategy": "originalfirst"}], "functions": {}, "showQuestionGroupNames": false, "tags": [], "ungrouped_variables": [], "preamble": {"js": "", "css": ""}, "metadata": {"description": "<p data-bind=\"html: 'hi'\">Ask the student to find a&nbsp;matrix corresponding to a given rotation about the origin.</p>\n<p data-bind=\"html: 'hi'\">Then ask them to find the determinant. Their answer is marked against the matrix they gave, not just the correct one.</p>\n<p data-bind=\"html: 'hi'\">Finally, ask them to find the inverse of their matrix. Marking is&nbsp;against the matrix and determinant they gave.</p>", "notes": "", "licence": "Creative Commons Attribution 4.0 International"}, "question_groups": [{"pickQuestions": 0, "pickingStrategy": "all-ordered", "questions": [], "name": ""}], "type": "question", "statement": "", "variablesTest": {"maxRuns": 100, "condition": ""}, "advice": "", "rulesets": {}}, {"name": "Adaptive marking: Independent two sample t-test", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["average", "data analysis", "differences", "elementary statistics", "hypothesis testing", "mean", "standard deviation", "statistics", "stats", "t-test", "two sample t-test", "variance"], "metadata": {"description": "<p>Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>An educational psychologist claimed that the order in which questions were asked affected the&nbsp;student&rsquo;s ability to answer them correctly and hence their total score. In order to test this, $20$ students were randomly divided into two groups of $10$. The first group were given questions&nbsp;in increasing order of difficulty and the second group in decreasing order of difficulty. The&nbsp;ordered test scores obtained were:</p>\n<table border=\"1\">\n<tbody>\n<tr><th align=\"left\">Group 1</th>\n<td>{r1[0]}</td>\n<td>{r1[1]}</td>\n<td>{r1[2]}</td>\n<td>{r1[3]}</td>\n<td>{r1[4]}</td>\n<td>{r1[5]}</td>\n<td>{r1[6]}</td>\n<td>{r1[7]}</td>\n<td>{r1[8]}</td>\n<td>{r1[9]}</td>\n</tr>\n<tr><th align=\"left\">Group 2</th>\n<td>{r2[0]}</td>\n<td>{r2[1]}</td>\n<td>{r2[2]}</td>\n<td>{r2[3]}</td>\n<td>{r2[4]}</td>\n<td>{r2[5]}</td>\n<td>{r2[6]}</td>\n<td>{r2[7]}</td>\n<td>{r2[8]}</td>\n<td>{r2[9]}</td>\n</tr>\n</tbody>\n</table>\n<p>Carry out a two-sample <em>t</em>-test to decide&nbsp;if there is evidence of a difference in the average&nbsp;test scores for the two sets of students.</p>", "advice": "<p>We test the following hypothesis,</p>\n<p style=\"text-align: center;\">$H_0:\\; \\mu_1=\\mu_2$ versus $H_1:\\; \\mu_1 \\neq \\mu_2$</p>\n<p>We find that the mean score of Group 1 is $\\overline{x}_1=\\var{mean1}$ with standard deviation $s_1=\\var{sd1}$ and the mean score of Group 2 is $\\overline{x}_2=\\var{mean2}$ with standard deviation $s_2=\\var{sd2}$.</p>\n<p>(All calculated to 3 decimal places.)</p>\n<p>Using the formula for the two-sample $t$-statistic as &nbsp;shown above with $n_1=n_2=10$:</p>\n<p>The estimate of the pooled variance is calculated to be:</p>\n<p>\\[s^2=\\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}= \\frac{\\var{n1-1}\\times \\var{sd1}^2+\\var{n2-1}\\times \\var{sd2}^2}{\\var{n1+n2-2}}=\\var{s^2}.\\]&nbsp;</p>\n<p>Hence $s = \\sqrt{\\var{s^2}}=\\var{s}$ to 3 decimal places.</p>\n<p>We find that the t-statistic has value:</p>\n<p>\\begin{align}<br/>T &amp;= \\frac{(\\overline{x}_1-\\overline{x}_2)-(\\mu_1-\\mu_2)}{s\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}} \\\\<br/>&amp;= \\frac{(\\var{mean1}-\\var{mean2})-(0)}{\\var{s}\\sqrt{\\frac{1}{\\var{n1}}+\\frac{1}{\\var{n2}}}} \\\\<br/>&amp;= \\var{t_statistic}<br/>\\end{align}</p>\n<p>Our test statistic is $|T|=\\var{abs(t_statistic)}$.</p>\n<p>Given that we have $n_1+n_2-2=18$ degrees of freedom, we look up this value on the T-distribution table for $t_{18}$</p>\n<p>\\[\\begin{array}{r|rrrrr}&amp;0.10&amp;0.05&amp;0.01&amp;0.001\\\\\\hline18&amp;1.734&amp;2.101&amp;2.878&amp;3.922\\end{array}\\]</p>\n<p>We see that the t-statistic {t_statistic_range} and the table tells us that the $p$ value {p_value_range}.</p>\n<p>Hence we conclude that we {reject} the null hypothesis. There is {evidence_strength} evidence of a difference between the average scores of the two groups.</p>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"p_value_range": {"name": "p_value_range", "group": "Advice messages", "definition": "['is less than $0.001$','lies between $0.001$ and $0.01$','lies between $0.01$ and $0.05$','lies between $0.05$ and $0.10$','is greater than $0.10$'][scenario]", "description": "<p>Describe where the p-value lies in relation to the critical values</p>", "templateType": "anything", "can_override": false}, "sigma2": {"name": "sigma2", "group": "Setup", "definition": "random(8..10#0.2)", "description": "<p>Population standard deviation of sample 2</p>", "templateType": "anything", "can_override": false}, "t99": {"name": "t99", "group": "Critical t-values", "definition": "2.878", "description": "", "templateType": "anything", "can_override": false}, "n2": {"name": "n2", "group": "Setup", "definition": "10", "description": "<p>Size of sample 2</p>", "templateType": "anything", "can_override": false}, "t999": {"name": "t999", "group": "Critical t-values", "definition": "3.922", "description": "", "templateType": "anything", "can_override": false}, "t_statistic_range": {"name": "t_statistic_range", "group": "Advice messages", "definition": "['is greater than $\\\\var{t999}$','lies between $\\\\var{t99}$ and $\\\\var{t999}$','lies between $\\\\var{t95}$ and $\\\\var{t99}$','lies between $\\\\var{t90}$ and $\\\\var{t95}$','is less than $\\\\var{t90}$'][scenario]", "description": "<p>Describe where the t-statistic lies in relation to the critical values</p>", "templateType": "anything", "can_override": false}, "mu2": {"name": "mu2", "group": "Setup", "definition": "random(65..75#0.5)", "description": "<p>Population mean of sample 2</p>", "templateType": "anything", "can_override": false}, "evidence_strength": {"name": "evidence_strength", "group": "Advice messages", "definition": "['very strong','strong','slight','no','no'][scenario]", "description": "<p>How much evidence is there against the null hypothesis?</p>", "templateType": "anything", "can_override": false}, "n1": {"name": "n1", "group": "Setup", "definition": "10", "description": "<p>Size of sample 1</p>", "templateType": "anything", "can_override": false}, "mu1": {"name": "mu1", "group": "Setup", "definition": "random(55..75#0.5)", "description": "<p>Population mean of sample 1 (we'll generate samples from different distributions to produce different outcomes)</p>", "templateType": "anything", "can_override": false}, "reject": {"name": "reject", "group": "Advice messages", "definition": "if(scenario<2,'do reject','do not reject')", "description": "<p>Do we reject the null hypothesis?</p>", "templateType": "anything", "can_override": false}, "p_value": {"name": "p_value", "group": "Stats", "definition": "ttest(abs(t_statistic),19,2)", "description": "<p>p-value&nbsp;corresponding to the t-statistic</p>", "templateType": "anything", "can_override": false}, "t_statistic": {"name": "t_statistic", "group": "Stats", "definition": "(mean1-mean2)*sqrt(n1*n2)/(s*sqrt(n1+n2))", "description": "", "templateType": "anything", "can_override": false}, "t90": {"name": "t90", "group": "Critical t-values", "definition": "1.734", "description": "", "templateType": "anything", "can_override": false}, "decision_marking_matrix": {"name": "decision_marking_matrix", "group": "Advice messages", "definition": "[\n  [1,0,0,0,0],\n  [0,1,0,0,0],\n  [0,0,1,0,0],\n  [0,0,0,1,0],\n  [0,0,0,0,1]\n][scenario]", "description": "<p>Marking matrix for the multiple choice questions</p>", "templateType": "anything", "can_override": false}, "sd2": {"name": "sd2", "group": "Stats", "definition": "precround(pstdev(r2),3)", "description": "<p>Sample standard deviation of sample 2</p>", "templateType": "anything", "can_override": false}, "t95": {"name": "t95", "group": "Critical t-values", "definition": "2.101", "description": "", "templateType": "anything", "can_override": false}, "r1": {"name": "r1", "group": "Samples", "definition": "repeat(round(normalsample(mu1,sigma1)),n1)", "description": "<p>Sample 1</p>", "templateType": "anything", "can_override": false}, "mean1": {"name": "mean1", "group": "Stats", "definition": "mean(r1)", "description": "<p>Sample mean of sample 1</p>", "templateType": "anything", "can_override": false}, "mean2": {"name": "mean2", "group": "Stats", "definition": "mean(r2)", "description": "<p>Sample&nbsp;mean of sample 1</p>", "templateType": "anything", "can_override": false}, "r2": {"name": "r2", "group": "Samples", "definition": "repeat(round(normalsample(mu2,sigma2)),n2)", "description": "<p>Sample 2</p>", "templateType": "anything", "can_override": false}, "scenario": {"name": "scenario", "group": "Advice messages", "definition": "sum(map(award(1,abs(t_statistic)<x),x,[t90,t95,t99,t999]))", "description": "<p>Which scenario are we in - how many critical values of the t distribution does t_statistic exceed?</p>", "templateType": "anything", "can_override": false}, "sigma1": {"name": "sigma1", "group": "Setup", "definition": "random(8..10#0.2)", "description": "<p>Population standard deviation of sample 1</p>", "templateType": "anything", "can_override": false}, "sd1": {"name": "sd1", "group": "Stats", "definition": "precround(pstdev(r1),3)", "description": "<p>Sample standard deviation of sample 1</p>", "templateType": "anything", "can_override": false}, "s": {"name": "s", "group": "Stats", "definition": "precround(sqrt(((n1-1)*sd1^2+(n2-1)*sd2^2)/(n1+n2-2)),3)", "description": "<p>Used in the&nbsp;formula for the t statistic</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Setup", "variables": ["n1", "n2", "mu1", "sigma1", "mu2", "sigma2"]}, {"name": "Samples", "variables": ["r1", "r2"]}, {"name": "Stats", "variables": ["mean1", "sd1", "mean2", "sd2", "s", "t_statistic", "p_value"]}, {"name": "Advice messages", "variables": ["scenario", "decision_marking_matrix", "reject", "evidence_strength", "t_statistic_range", "p_value_range"]}, {"name": "Critical t-values", "variables": ["t90", "t95", "t99", "t999"]}], "functions": {"pstdev": {"parameters": [["l", "list"]], "type": "number", "language": "jme", "definition": "sqrt(len(l)/(len(l)-1))*stdev(l)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the mean and standard deviations of the scores of the two groups.&nbsp;Round your answers to 3 decimal places.</p>\n<table>\n<thead>\n<tr>\n<th></th>\n<th>Mean</th>\n<th>Standard deviation</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n<th>Group 1</th>\n<td>[[0]]</td>\n<td>[[1]]</td>\n</tr>\n<tr>\n<th>Group 2</th>\n<td>[[2]]</td>\n<td>[[3]]</td>\n</tr>\n</tbody>\n</table>\n<p>Now find the two sample <em>t</em>-test statistic $T$ using the values you have just calculated and enter it here: [[4]]</p>", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The two-sample <em>t</em>-statistic for two independent sets of data where one set has $n_1$ data points and the other set $n_2$ data points is calculated as follows:</p>\n<p>\\[T = \\frac{(\\overline{x}_1-\\overline{x}_2)-(\\mu_1-\\mu_2)}{s\\times\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}}\\;\\;\\;\\]</p>\n<p>where $\\overline{x}_1,\\;\\overline{x}_2$ are the sample means and&nbsp;</p>\n<p>\\[s^2=\\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}\\]</p>\n<p>where $s_1,\\;s_2$ are the sample standard deviations.</p>\n<p>Use the values you calculated to 3 decimal places in order to find $T$.</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 0.5, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "mean1", "maxValue": "mean1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 0.5, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "sd1", "maxValue": "sd1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 0.5, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "mean2", "maxValue": "mean2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 0.5, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "sd2", "maxValue": "sd2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "mean1", "part": "p0g0", "must_go_first": false}, {"variable": "sd1", "part": "p0g1", "must_go_first": false}, {"variable": "mean2", "part": "p0g2", "must_go_first": false}, {"variable": "sd2", "part": "p0g3", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "t_statistic", "maxValue": "t_statistic", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "t_statistic", "part": "p0g4", "must_go_first": false}], "variableReplacementStrategy": "alwaysreplace", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Given the value $|T|$ of the <em>t</em>-statistic you have found, choose the range for the $p$ value by looking up the <em>t</em>&nbsp;tables:</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["<p>$p$ is less than $0.1\\%$</p>", "<p>$p$ lies between $0.1\\%$ and $1\\%$</p>", "<p>$p$ lies between  $1 \\%$ and $5\\%$</p>", "<p>$p$ lies between  $5 \\%$ and $10\\%$</p>", "<p>$p$ is greater than $10\\%$</p>"], "matrix": "decision_marking_matrix"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "scenario", "part": "p1", "must_go_first": false}], "variableReplacementStrategy": "alwaysreplace", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Given the $p$-value and the range you have found, what is the strength of evidence against the null hypothesis that there is no difference in the average times for the left and right hands?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>Very Strong Evidence</p>", "<p>Strong Evidence</p>", "<p>Evidence</p>", "<p>Weak Evidence</p>", "<p>No Evidence</p>"], "matrix": "decision_marking_matrix"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "scenario", "part": "p2", "must_go_first": false}], "variableReplacementStrategy": "alwaysreplace", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What do you&nbsp;decide&nbsp;based on the above analysis?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["<p>We reject the null hypothesis at the $0.1\\%$ level</p>", "<p>We reject the null hypothesis at the $1\\%$ level.</p>", "<p>We reject the null hypothesis at the $5\\%$ level.</p>", "<p>We do not reject the null hypothesis but consider further investigation.</p>", "<p>We do not reject the null hypothesis.</p>"], "matrix": "decision_marking_matrix"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "BMI calculations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "tags": ["ephlth", "nursing"], "metadata": {"description": "<p>Given the formula&nbsp;for BMI, students are asked to determine a patient's BMI given their height in cm (as people usually do) and their mass in kg.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Calculate the following <strong>with the use</strong> of a calculator.</p>", "advice": "", "rulesets": {}, "variables": {"upordown": {"name": "upordown", "group": "Ungrouped variables", "definition": "if(bmi6dec>bmi,\"down\",if(bmi6dec<bmi,\"up\",\"\"))", "description": "", "templateType": "anything"}, "height": {"name": "height", "group": "Ungrouped variables", "definition": "random(150..190)", "description": "", "templateType": "anything"}, "bmi6dec": {"name": "bmi6dec", "group": "Ungrouped variables", "definition": "precround(10000*mass/(height^2),6)", "description": "", "templateType": "anything"}, "bmi": {"name": "bmi", "group": "Ungrouped variables", "definition": "precround(10000*mass/(height^2),2)", "description": "", "templateType": "anything"}, "mass": {"name": "mass", "group": "Ungrouped variables", "definition": "random(60..130)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["mass", "height", "bmi", "bmi6dec", "upordown"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A patient has a height of $\\var{height}$ cm&nbsp;and weighs $\\var{mass}$ kg.&nbsp;</p>\n<p>The&nbsp;formula for BMI (Body Mass Index) is</p>\n<p>\\[\\text{BMI}=\\frac{\\text{mass (kg)}}{\\text{height (m)}^2}.\\]&nbsp;</p>\n<p>The patient's BMI to two decimal places is&nbsp;[[0]].</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The equation for BMI&nbsp;is</p>\n<p>\\[\\text{BMI}=\\frac{\\text{mass (kg)}}{\\text{height (m)}^2}\\]&nbsp;</p>\n<p>Notice the units in the formula are kilograms and metres. We convert the $\\var{height}$ cm into metres by moving the decimal point twice to the left to get $\\var{height/100}$ m.&nbsp;</p>\n<p>Using a scientific calculator you&nbsp;can type in \\[\\var{mass}\\div \\var{height/100}^2\\] or by using the fraction button you may be able to type in&nbsp;\\[\\frac{\\var{mass}}{\\var{height/100}^2}\\] and it will give you something like $\\var{bmi6dec}$ which you need to round {upordown} to two decimal places and get <span data-jme-visible=\"mod(bmi*10,1)&lt;&gt;0\">$\\var{bmi}$</span>&nbsp;<span data-jme-visible=\"mod(bmi*10,1)=0 and mod(bmi,1)&lt;&gt;0\">$\\var{bmi}0$</span>&nbsp;<span data-jme-visible=\"mod(bmi,1)=0\">$\\var{bmi}.00$</span></p>\n<p></p>\n<p></p>\n<p>A few things to remark:</p>\n<ul>\n<li>Since the height is given in centimetres you would need to know there <g class=\"gr_ gr_67 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace\" id=\"67\" data-gr-id=\"67\">are</g> $100$ cm in $1$ m, so for example, $183$ cm would be $1.83$ m.</li>\n<li>If you were using a non-scientific calculator you would need to know that squaring the height must happen&nbsp;before the division, that is you would need to use brackets as so, $\\var{mass}\\div \\left(\\var{height/100}^2\\right)$.</li>\n<li>If you had a pocket calculator you may need to know that $\\text{height}^2=\\text{height}\\times\\text{height}$ and you would have to do a few separate calculations one after the other, or you could do $(\\var{mass}\\div\\var{height/100})\\div\\var{height/100}$.</li>\n</ul>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{bmi}", "maxValue": "{bmi}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Concentration: percentage weight per volume", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "tags": ["concentration", "ephlth", "nursing"], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"marking": {"name": "marking", "group": "b", "definition": "[if(mult=1,1,0),if(mult=2,1,0),0,if(mult=10,1,0)]", "description": "", "templateType": "anything"}, "ans2": {"name": "ans2", "group": "b", "definition": "mult*100", "description": "", "templateType": "anything"}, "gramsb": {"name": "gramsb", "group": "whole numbers that result in simple decimal", "definition": "ansb*2*k", "description": "", "templateType": "anything"}, "grams": {"name": "grams", "group": "Ungrouped variables", "definition": "random(0.1..20#0.1)", "description": "", "templateType": "anything"}, "k": {"name": "k", "group": "whole numbers that result in simple decimal", "definition": "random(2..12)", "description": "", "templateType": "anything"}, "mill": {"name": "mill", "group": "Ungrouped variables", "definition": "random(50..1000#50)", "description": "", "templateType": "anything"}, "list": {"name": "list", "group": "b", "definition": "[100,200,500,1000]", "description": "", "templateType": "anything"}, "gramsnice": {"name": "gramsnice", "group": "Ungrouped variables", "definition": "ansnice*fudge", "description": "", "templateType": "anything"}, "per": {"name": "per", "group": "b", "definition": "random(0.1..10#0.1)", "description": "", "templateType": "anything"}, "ansnice": {"name": "ansnice", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "", "templateType": "anything"}, "amount": {"name": "amount", "group": "b", "definition": "mult*per", "description": "", "templateType": "anything"}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "precround(test,2)", "description": "", "templateType": "anything"}, "test": {"name": "test", "group": "Ungrouped variables", "definition": "grams/mill*100\n", "description": "", "templateType": "anything"}, "millnice": {"name": "millnice", "group": "Ungrouped variables", "definition": "100*fudge", "description": "", "templateType": "anything"}, "ansb": {"name": "ansb", "group": "whole numbers that result in simple decimal", "definition": "random(0.5..10.5#1)", "description": "", "templateType": "anything"}, "chem": {"name": "chem", "group": "Ungrouped variables", "definition": "shuffle([\"$\\\\text{NaCl}$\",\"$\\\\text{KCl}$\",\"$\\\\mathrm{C_3H_5NaO_3}$\",\"$\\\\mathrm{CaCl_2.2H_2O}$\",\"$\\\\mathrm{Ca_3PO_4}$\",\"$\\\\mathrm{MgCl_2}$\",\"$\\\\mathrm{Na_2HPO_4}$\",\"$\\\\mathrm{Na_2SO_4}$\"])[0..4]", "description": "", "templateType": "anything"}, "fudge": {"name": "fudge", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything"}, "millb": {"name": "millb", "group": "whole numbers that result in simple decimal", "definition": "100*2*k", "description": "", "templateType": "anything"}, "mult": {"name": "mult", "group": "b", "definition": "random(1,2,10)", "description": "", "templateType": "anything"}, "ansr": {"name": "ansr", "group": "Ungrouped variables", "definition": "precround(ans,2)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["mill", "grams", "chem", "test", "ans", "millnice", "gramsnice", "ansnice", "fudge", "ansr"], "variable_groups": [{"name": "b", "variables": ["per", "mult", "amount", "ans2", "marking", "list"]}, {"name": "whole numbers that result in simple decimal", "variables": ["ansb", "millb", "gramsb", "k"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A {millnice} mL solution is made by mixing {gramsnice} g of {chem[2]} and water. The percentage weight per volume of the solution is [[0]]&nbsp;% w/v of {chem[2]}.</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Percentage weight per volume is the weight of the&nbsp;solute in grams divided by&nbsp;the amount of solution in millilitres expressed as a percentage. That is, we do the division and multiply by 100.</p>\n<p></p>\n<p>In particular, if a {millnice} mL solution is made by mixing {gramsnice} g of {chem[2]} and water. The percentage weight per volume of the solution is:</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\dfrac{\\text{grams}}{\\text{millilitres}}\\times 100$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\dfrac{\\var{gramsnice}}{\\var{millnice}}\\times 100$ % w/v</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\var{ansnice}$ % w/v&nbsp;</td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ansnice", "maxValue": "ansnice", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A {millb} mL solution is made by mixing {gramsb} g of {chem[3]} and water. The percentage weight per volume of the solution is [[0]]&nbsp;% w/v of {chem[3]}.</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Percentage weight per volume is the weight of the&nbsp;solute in grams divided by&nbsp;the amount of solution in millilitres expressed as a percentage. That is, we do the division and multiply by 100.</p>\n<p></p>\n<p>In particular, if a {millb} mL solution is made by mixing {gramsb} g of {chem[3]} and water. The percentage weight per volume of the solution is:</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\dfrac{\\text{grams}}{\\text{millilitres}}\\times 100$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\dfrac{\\var{gramsb}}{\\var{millb}}\\times 100$ % w/v</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\var{ansb}$ % w/v&nbsp;</td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ansb", "maxValue": "ansb", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A {mill} mL solution is made by mixing {grams} g of {chem[0]} and water. The percentage weight per volume of the solution is [[0]]&nbsp;% w/v of {chem[0]} (to 2 decimal places).</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Percentage weight per volume is the weight of the&nbsp;solute in grams divided by&nbsp;the amount of solution in millilitres expressed as a percentage. That is, we do the division and multiply by 100.</p>\n<p></p>\n<p>In particular, if a {mill} mL solution is made by mixing {grams} g of {chem[0]} and water. The percentage weight per volume of the solution is:</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\dfrac{\\text{grams}}{\\text{millilitres}}\\times 100$</td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\dfrac{\\var{grams}}{\\var{mill}}\\times 100$ % w/v</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\">$=$</td>\n<td style=\"text-align: left;\">$\\var{ans}$ % w/v&nbsp; (to 2 dec. pl)</td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ansr", "maxValue": "ansr", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A {per}&nbsp;% {chem[1]} solution contains {amount} g of {chem[1]} in every...</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>It is important to know&nbsp;{per}&nbsp;% {chem[1]} solution contains {per} g of {chem[1]} in every 100 mL of solution.</p>\n<p></p>\n<p><span data-jme-visible=\"mult=2\">Given this,&nbsp;since&nbsp;we have {amount} g of {chem[1]}&nbsp;we have&nbsp;two times the standard amount and so we must have two times the solution, that is 200 mL.</span></p>\n<p></p>\n<p><span data-jme-visible=\"mult=10\">Given this,&nbsp;since&nbsp;we have {amount} g of {chem[1]}&nbsp;we have&nbsp;ten times the standard amount and so we must have ten times the solution, that is 1000 mL.</span></p>"}], "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>100 mL.</p>", "<p>200 mL.</p>", "<p>500 mL.</p>", "<p>1000 mL.</p>"], "matrix": "marking"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}], "pickQuestions": 0, "pickingStrategy": "all-ordered", "name": ""}], "shuffleQuestions": false, "duration": 0, "type": "exam", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "extensions": ["stats"], "custom_part_types": [], "resources": []}