// Numbas version: exam_results_page_options
{"name": "ANOVA (one-way): alcohol effect", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "ANOVA (one-way): alcohol effect", "tags": [], "metadata": {"description": "<p>This question assesses learners' basic knowledge of a one-way ANOVA and ability to interpret typical software output.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>A study was conducted to investigate any effect of alcohol consumption on the time taken to complete a cognitive task (involving mental arithmetic). 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. The following table reports the responses as the times (in seconds) taken to complete the task:</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<th align=\"left\">Group A (0 units)</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</tr>\n<tr>\n<th align=\"left\">Group B (2 units)</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</tr>\n<tr>\n<th align=\"left\">Group C (4 units)</th>\n<td>{r3[0]}</td>\n<td>{r3[1]}</td>\n<td>{r3[2]}</td>\n<td>{r3[3]}</td>\n<td>{r3[4]}</td>\n<td>{r3[5]}</td>\n</tr>\n</tbody>\n</table>\n<p>Complete the sections below to test and evaluate the null hypothesis that alcohol consumption does not affect the mean time taken to complete the task.</p>\n<p>&nbsp;</p>", "advice": "<p>Revise ANOVA, e.g., Section 7.5 of&nbsp;<a href=\"https://leanpub.com/openintro-statistics\">OpenIntro Statistics</a>&nbsp;(4th edition).</p>\n<p>The p-value can be calculated from the F value using Excel's&nbsp;F.DIST.RT function.</p>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "extensions": ["stats"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"rss": {"name": "rss", "group": "Ungrouped variables", "definition": "siground(ss-stovern,3)", "description": "", "templateType": "anything", "can_override": false}, "r3": {"name": "r3", "group": "Ungrouped variables", "definition": "repeat(round(normalsample(mu3,sig3)),6)", "description": "", "templateType": "anything", "can_override": false}, "sig2": {"name": "sig2", "group": "Ungrouped variables", "definition": "sig1", "description": "", "templateType": "anything", "can_override": false}, "mu1": {"name": "mu1", "group": "Ungrouped variables", "definition": "random(20..25#0.5)", "description": "", "templateType": "anything", "can_override": false}, "sd1": {"name": "sd1", "group": "Ungrouped variables", 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"group": "Ungrouped variables", "definition": "sum(ssq)", "description": "", "templateType": "anything", "can_override": false}, "pvalue": {"name": "pvalue", "group": "Ungrouped variables", "definition": "precround(ftest(VR,2,15),3)", "description": "", "templateType": "anything", "can_override": false}, "sig1": {"name": "sig1", "group": "Ungrouped variables", "definition": "random(3..5#0.2)", "description": "", "templateType": "anything", "can_override": false}, "sd3": {"name": "sd3", "group": "Ungrouped variables", "definition": "precround(pstdev(r3),2)", "description": "", "templateType": "anything", "can_override": false}, "cmsg": {"name": "cmsg", "group": "Ungrouped variables", "definition": "['do reject','do reject','do not reject','do not reject','do not reject']", "description": "", "templateType": "anything", "can_override": false}, "sd2": {"name": "sd2", "group": "Ungrouped variables", "definition": "precround(pstdev(r2),2)", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "sum(t)", "description": "", "templateType": "anything", "can_override": false}, "dfbt": {"name": "dfbt", "group": "Ungrouped variables", "definition": "k-1", "description": "", "templateType": "anything", "can_override": false}, "ssq": {"name": "ssq", "group": "Ungrouped variables", "definition": "[sum(map(x^2,x,r1)),sum(map(x^2,x,r2)),sum(map(x^2,x,r3))]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["sd1", "sd2", "sd3", "vr", "mbt", "pmsg", "mu3", "stderror", "n", "m1", "tol", "m2", "btss", "stovern", "tss", "dfbt", "m3", "ssq", "sig1", "v1", "sig3", "sig2", "dfrs", "cmsg", "rss", "tsqovern", "mu1", "g", "r2", "mu2", "ss", "k", "r3", "mrs", "r1", "u", "t", "v", "n1", "n2", "n3", "pvalue"], "variable_groups": [], "functions": {"pstdev": {"parameters": [["l", "list"]], "type": "number", "language": "jme", "definition": "sqrt(abs(l)/(abs(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>Fill in the gaps in this table of descriptive statistics:</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td>&nbsp;</td>\n<td>$\\overline{x}_i$</td>\n<td>$SD_i$</td>\n<td>$n_i$</td>\n</tr>\n<tr>\n<th align=\"left\">Group A</th>\n<td>[[0]]</td>\n<td>[[1]]</td>\n<td>6</td>\n</tr>\n<tr>\n<th align=\"left\">Group B</th>\n<td>[[2]]</td>\n<td>[[3]]</td>\n<td>6</td>\n</tr>\n<tr>\n<th align=\"left\">Group C</th>\n<td>[[4]]</td>\n<td>[[5]]</td>\n<td>6</td>\n</tr>\n<tr>\n<td>&nbsp;</td>\n<td>&nbsp;</td>\n<td>&nbsp;</td>\n<td>$N=18$</td>\n</tr>\n</tbody>\n</table>", "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": "m1*(1-tol)", "maxValue": "m1*(1+tol)", "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": "sd1*(1-tol)", "maxValue": "sd1*(1+tol)", "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": "m2*(1-tol)", "maxValue": "m2*(1+tol)", "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": "sd2*(1-tol)", "maxValue": "sd2*(1+tol)", "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": "m3*(1-tol)", "maxValue": "m3*(1+tol)", "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": "sd3*(1-tol)", "maxValue": "sd3*(1+tol)", "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>Fill in the gaps in the ANOVA table:</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<th align=\"left\"></th>\n<th>df</th>\n<th>Sum Sq</th>\n<th>Mean Sq</th>\n<th>F</th>\n</tr>\n<tr>\n<th align=\"left\">alcohol</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\">Residuals</th>\n<td>[[4]]</td>\n<td>[[5]]</td>\n<td>$\\var{mrs}$</td>\n<td>-</td>\n</tr>\n<tr>\n<th align=\"left\">Total</th>\n<td>[[6]]</td>\n<td>$\\var{tss}$</td>\n<td>-</td>\n<td>-</td>\n</tr>\n</tbody>\n</table>\n<p></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*(1-tol)", "maxValue": "dfbt*(1+tol)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", 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"displayAnswer": "", "showFractionHint": true, "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": "dfrs*(1-tol)", "maxValue": "dfrs*(1+tol)", "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": [], 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