// Numbas version: exam_results_page_options
{"name": "Hypothesis test (volume)", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Hypothesis test (volume)", "tags": [], "metadata": {"description": "<p>Provided with information on a sample (&gt;30) with sample mean and standard deviation, use the z test to either accept or reject a given null hypothesis.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>A leading manufacturer claims its product contains {thisamount} ml by volume. A sample of {n}&nbsp;items was taken and the mean of the sample was $\\bar{x}=\\var{m}$ ml and the standard deviation of the sample was $s = \\var{stand}$ ml. Is the manufacturers claim justified?</p>\n<p><em><strong></strong></em></p>", "advice": "<p>a)</p>\n<p><strong>Step 1: Null Hypothesis</strong></p>\n<p>$\\operatorname{H}_0\\;: \\; \\mu=\\;\\var{thisamount}$</p>\n<p><strong>Step 2: Alternative Hypothesis</strong></p>\n<p>$\\operatorname{H}_1\\;: \\; \\mu \\neq\\;\\var{thisamount}$</p>\n<p>b)</p>\n<p>We should use the z statistic since the sample size is greater than 30.</p>\n<p>The test statistic:</p>\n<p>\\[z = \\frac{\\var{m}-\\var{thisamount}}{\\frac{\\var{stand}}{\\sqrt{\\var{n}}}}=\\var{teststatistic}\\]</p>\n<p>to 3 decimal places.</p>\n<p>c)</p>\n<p>&nbsp;For a significance level of 5%:</p>\n<p>$z_{{\\frac{\\alpha}{2}}}=\\var{critical}$</p>\n<p></p>\n<p><strong><br/></strong>d)</p>\n<p>Hence there is {evi1[pval]} evidence against $\\operatorname{H}_0$ and so we {dothis}&nbsp;$\\operatorname{H}_0$.</p>\n<p>{Correctc}</p>", "rulesets": {}, "extensions": ["stats"], "variables": {"m": {"name": "m", "group": "Ungrouped variables", "definition": "thisamount+random(0.2..0.6#0.02)", "description": "", "templateType": "anything"}, "fac": {"name": "fac", "group": "Ungrouped variables", "definition": "if(abs(teststatistic)>abs(critical),\"There is insufficient evidence against the claim of the manufacturer\",\"There is sufficient evidence against the claim of the manufacturer.\")", "description": "", "templateType": "anything"}, "tol": {"name": "tol", "group": "Ungrouped variables", "definition": "0.001", "description": "", "templateType": "anything"}, "evi1": {"name": "evi1", "group": "Ungrouped variables", "definition": "[\"sufficient\",\"insufficient\"]", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(35..45)", "description": "", "templateType": "anything"}, "dmm": {"name": "dmm", "group": "Ungrouped variables", "definition": "if(pval=1,[1,0],[0,1])", "description": "", "templateType": "anything"}, "mm": {"name": "mm", "group": "Ungrouped variables", "definition": "switch(pval=0,[1,0,0,0],pval=1,[0,1,0,0],pval=2,[0,0,1,0],[0,0,0,1])", "description": "", "templateType": "anything"}, "zval1": {"name": "zval1", "group": "Ungrouped variables", "definition": "abs(m-thisamount)*sqrt(n)/stand", "description": "", "templateType": "anything"}, "zval": {"name": "zval", "group": "Ungrouped variables", "definition": "precround(zval1,3)", "description": "", "templateType": "anything"}, "pval": {"name": "pval", "group": "Ungrouped variables", "definition": "switch(abs(zval)>1.96,0,1)", "description": "", "templateType": "anything"}, "evi": {"name": "evi", "group": "Ungrouped variables", "definition": "[\"None\",\"Slight\",\"Moderate\",\"Strong\"]", "description": "", "templateType": "anything"}, "teststatistic": {"name": "teststatistic", "group": "Ungrouped variables", "definition": "precround(if(m-thisamount>0,zval1,-zval1),3)", "description": "", "templateType": "anything"}, "dothis": {"name": "dothis", "group": "Ungrouped variables", "definition": "switch(abs(teststatistic)<abs(critical), 'fail to reject','reject')", "description": "", "templateType": "anything"}, "stand": {"name": "stand", "group": "Ungrouped variables", "definition": "random(0.8..1#0.01)", "description": "", "templateType": "anything"}, "correctc": {"name": "correctc", "group": "Ungrouped variables", "definition": "if(abs(teststatistic)<abs(critical),\"There is insufficient evidence against the claim of the manufacturer\",\"There is sufficient evidence against the claim of the manufacturer.\")", "description": "", "templateType": "anything"}, "thisamount": {"name": "thisamount", "group": "Ungrouped variables", "definition": "random(35..40#0.1)", "description": "", "templateType": "anything"}, "critical": {"name": "critical", "group": "Ungrouped variables", "definition": "if(m-thisamount>0,1.96,-1.96)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pval", "evi1", "zval1", "stand", "tol", "fac", "evi", "dothis", "correctc", "m", "dmm", "n", "mm", "thisamount", "zval", "teststatistic", "critical"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p><strong>Step 1: Null Hypothesis</strong></p>\n<p>$\\operatorname{H}_0\\;: \\; \\mu=\\;$[[0]]</p>\n<p><strong>Step 2: Alternative Hypothesis</strong></p>\n<p>$\\operatorname{H}_1\\;: \\; \\mu \\neq\\;$[[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 0.5, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "thisamount", "maxValue": "thisamount", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 0.5, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "thisamount", "maxValue": "thisamount", "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, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p><strong>Step 3: Test statistic</strong></p>\n        <p>Should we use the z or t test statistic? [[0]] (enter z or t).</p>\n        <p>Now calculate the test statistic = ? [[1]] (to 3 decimal places)</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "z", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "z", "value": ""}]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "teststatistic-tol", "maxValue": "teststatistic+tol", "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, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p><strong>Step 4: critical value</strong></p>\n<p>Use tables to find the critical value for a significance level of 5%.&nbsp;</p>\n<p>[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "critical", "maxValue": "critical", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p><strong></strong></p>\n<p><strong>Your Decision:</strong></p>\n<p><strong>[[0]]</strong></p>\n<p></p>\n<p><strong>&nbsp;</strong></p>\n<p><strong>Conclusion:</strong></p>\n<p><strong>[[1]]</strong></p>\n<p></p>", "gaps": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["Fail to reject", "Reject"], "matrix": "dmm"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["{Correctc}", "{Fac}"], "matrix": [1, 0], "distractors": ["", ""]}], "sortAnswers": false}], "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}, {"name": "Patrice Behan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1791/"}]}]}], "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}, {"name": "Patrice Behan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1791/"}]}