// Numbas version: exam_results_page_options
{"name": "Perform a one-way ANOVA", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Perform a one-way ANOVA", "tags": [], "metadata": {"description": "<p>One-way ANOVA example</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>The following data arose in a comparison of the effects of alcohol on the time taken to complete a task. There were three groups of subjects: Group A had no alcohol, Group B had two units over 1 hour and Group C had 4 units over 1 hour.&nbsp;</p>\n<p>The responses are the times (in seconds) taken to&nbsp;complete a&nbsp;martial arts \"coloured ball\"&nbsp;drill, in which the subjects respond to different coloured balls pulled from a bucket with different actions (e.g. kick, punch), as quickly as possible.</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<th align=\"left\">Group A (0 units)</th>\n<td>$\\var{r1[0]}$</td>\n<td>$\\var{r1[1]}$</td>\n<td>$\\var{r1[2]}$</td>\n<td>$\\var{r1[3]}$</td>\n<td>$\\var{r1[4]}$</td>\n<td>$\\var{r1[5]}$</td>\n</tr>\n<tr>\n<th align=\"left\">Group B (2 units)</th>\n<td>$\\var{r2[0]}$</td>\n<td>$\\var{r2[1]}$</td>\n<td>$\\var{r2[2]}$</td>\n<td>$\\var{r2[3]}$</td>\n<td>$\\var{r2[4]}$</td>\n<td>$\\var{r2[5]}$</td>\n</tr>\n<tr>\n<th align=\"left\">Group C (4 units)</th>\n<td>$\\var{r3[0]}$</td>\n<td>$\\var{r3[1]}$</td>\n<td>$\\var{r3[2]}$</td>\n<td>$\\var{r3[3]}$</td>\n<td>$\\var{r3[4]}$</td>\n<td>$\\var{r3[5]}$</td>\n</tr>\n</tbody>\n</table>\n<ul>\n<li>Write down the sample mean and standard deviation for each group together with an estimate of the standard error of a mean, $\\displaystyle\\frac{s}{\\sqrt{n}}$, to 2 decimal places.</li>\n<li>Test the null hypothesis that the alcohol consumption does not affect the mean time taken to complete the task.</li>\n</ul>\n<p>&nbsp;</p>", "advice": "<h4>a)</h4>\n<p>Here we will work through the top row of the table and compute the values for Group $A$. The other two rows are calculated in the same way.</p>\n<p style=\"text-align: left;\">\\[ T = \\var{r1[0]}+\\var{r1[1]}+\\var{r1[2]}+\\var{r1[3]}+\\var{r1[4]}+\\var{r1[5]}=\\var{t[0]}. \\]</p>\n<p style=\"text-align: left;\">\\[\\bar{x} = \\frac{T}{6}=\\var{m1}.\\]</p>\n<p style=\"text-align: left;\">\\[&nbsp;\\sum{x^2}=\\var{r1[0]}^2+\\var{r1[1]}^2+\\var{r1[2]}^2+\\var{r1[3]}^2+\\var{r1[4]}^2+\\var{r1[5]}^2 =\\var{ssq[0]}.\\]</p>\n<p style=\"text-align: left;\">\\begin{align} <br/>s &amp;= \\sqrt{\\frac{1}{n-1}\\left(\\sum_{i=1}^{n}x_i^2 -n\\bar{x}^2\\right)} \\\\<br/>&amp;= \\sqrt{\\frac{1}{5}(\\var{ssq[0]}-6\\times\\var{m1})} \\\\<br/>&amp;= \\var{sd1}.<br/>\\end{align}</p>\n<p></p>\n<h4>b)</h4>\n<p>$\\displaystyle TSS$ is the total sum of squares of the ${3}$ groups minus the total sum of the ${3}$ groups divided by the total number of subjects.&nbsp;</p>\n<p>\\[ TSS =\\var{ss}-\\frac{\\var{g}}{18}=\\var{tss}. \\]</p>\n<p>Similarly</p>\n<p>\\[ BTSS=\\var{btss} \\]</p>\n<p>\\[ RSS=\\var{rss} \\]</p>\n<p></p>\n<h4>c)</h4>\n<p>The ANOVA table can be completed from the above values:</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<th align=\"left\">Source</th>\n<th>df</th>\n<th>SS</th>\n<th>MS</th>\n<th>VR</th>\n</tr>\n<tr>\n<th align=\"left\">Between Treatments</th>\n<td>{{dfbt}}</td>\n<td>{{btss}}</td>\n<td>{{mbt}}</td>\n<td>{{vr}}</td>\n</tr>\n<tr>\n<th align=\"left\">Residual</th>\n<td>{{dfrs}}</td>\n<td>{{rss}}</td>\n<td>{{mrs}}</td>\n<td>-</td>\n</tr>\n<tr>\n<th align=\"left\">Total</th>\n<td>{{n-1}}</td>\n<td>{{tss}}</td>\n<td>-</td>\n<td>-</td>\n</tr>\n</tbody>\n</table>\n<p>The estimated standard error of the mean is {{stderror}}.</p>\n<h4></h4>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "extensions": ["stats"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"t": {"name": "t", "group": "Ungrouped variables", "definition": "[sum(r1),sum(r2),sum(r3)]", "description": 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"minValue": "g", "maxValue": "g", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "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": "ss", "maxValue": "ss", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "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": "\n      <p>Now find the following, all to 2 decimal places:</p>\n        <p>$\\displaystyle TSS\\;=\\;$[[0]],&nbsp;$\\displaystyle BTSS\\;=\\;$[[1]],&nbsp;$\\displaystyle RSS\\;=\\;$[[2]]</p>\n      ", "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": "tss", "maxValue": "tss", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "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": "btss", "maxValue": "btss", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "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": "rss", "maxValue": "rss", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "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>Now complete the ANOVA table using the values to 2 decimal places obtained above:</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<th align=\"left\">Source</th>\n<th>df</th>\n<th>SS</th>\n<th>MS</th>\n<th>VR</th>\n</tr>\n<tr>\n<th align=\"left\">Between Treatments</th>\n<td>[[0]]</td>\n<td>[[1]]</td>\n<td>[[2]]</td>\n<td>[[3]]</td>\n</tr>\n<tr>\n<th align=\"left\">Residual</th>\n<td>[[4]]</td>\n<td>[[5]]</td>\n<td>[[6]]</td>\n<td>-</td>\n</tr>\n<tr>\n<th align=\"left\">Total</th>\n<td>[[7]]</td>\n<td>[[8]]</td>\n<td>-</td>\n<td>-</td>\n</tr>\n</tbody>\n</table>\n<p>Also calculate the estimated standard error of the mean : [[9]]</p>\n<p>Note that <strong>VR&nbsp;</strong>is found by taking the ratio of two of the values in this table.</p>\n<p>Input all numbers to 2 decimal places.</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": "dfbt", "maxValue": "dfbt", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "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": "btss", "maxValue": "btss", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "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": "mbt", "maxValue": "mbt", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "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": "vr", "maxValue": "vr", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "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": "dfrs", "maxValue": "dfrs", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "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": "rss", "maxValue": "rss", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "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": "mrs", "maxValue": "mrs", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "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": "n-1", "maxValue": "n-1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "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": "tss", "maxValue": "tss", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "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": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "stderror-tol", "maxValue": "stderror+tol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "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": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Given the value of $VR$ you have found, choose the range for the $p$ value by looking up the critical values of $F_{2,15}$ (one-sided).</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td>$10\\%$</td>\n<td>$5\\%$</td>\n<td>$1\\%$</td>\n<td>$0.1\\%$</td>\n</tr>\n<tr>\n<td>$2.70$</td>\n<td>$3.68$</td>\n<td>$6.36$</td>\n<td>$11.34$</td>\n</tr>\n</tbody>\n</table>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 1, "showCellAnswerState": true, "choices": ["<p>$p$ 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": "v"}, {"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>Given the $p$-value and the range you have found, what is the strength of evidence against the null hypothesis that the mean times taken are the same for the three groups?</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": "v"}, {"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>Hence what is your decision based on the above ANOVA 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": "v"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Vicky Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/659/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Tom Lowe", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9601/"}, {"name": "Pete Philipson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/13881/"}]}]}], "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Vicky Hall", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/659/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Tom Lowe", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9601/"}, {"name": "Pete Philipson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/13881/"}]}