// Numbas version: finer_feedback_settings
{"name": "CorrelationInference-Couples", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "CorrelationInference-Couples", "tags": [], "metadata": {"description": "<p>Calculate the Pearson correlation coefficient and conduct a hypothesis test.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>It is well known that similarity in attitudes, beliefs and interests plays an important role in interpersonal attraction. A researcher developed a questionnaire which was completed by 8 married couples. One question sought to place each individual on a 20 point scale in which low scores represent liberal attitudes and high scores represent conservative attitudes. The data were:</p>\n<table border=\"0\" cellpadding=\"0\" cellspacing=\"0\" style=\"border-collapse: collapse; width: 314px;\"><colgroup><col width=\"64\" span=\"3\" style=\"width: 48pt;\"/> </colgroup>\n<tbody>\n<tr height=\"20\" style=\"height: 15.0pt;\">\n<td height=\"20\" style=\"height: 15pt; width: 62px;\">Couple</td>\n<td style=\"width: 98px;\">Wife $(x)$</td>\n<td style=\"width: 111px;\">Husband $(y)$</td>\n</tr>\n<tr height=\"20\" style=\"height: 15.0pt;\">\n<td height=\"20\" style=\"height: 15pt; text-align: center; width: 62px;\">{obj[0]}</td>\n<td style=\"padding-bottom: 4px; padding-top: 4px; width: 98px;\">{r1[0]}</td>\n<td style=\"padding-bottom: 4px; padding-top: 4px; width: 111px;\">{r2[0]}</td>\n</tr>\n<tr height=\"20\" style=\"height: 15.0pt;\">\n<td height=\"20\" style=\"height: 15pt; text-align: center; width: 62px;\">{obj[1]}</td>\n<td style=\"padding-bottom: 4px; padding-top: 4px; width: 98px;\">{r1[1]}</td>\n<td style=\"padding-bottom: 4px; padding-top: 4px; width: 111px;\">{r2[1]}</td>\n</tr>\n<tr height=\"20\" style=\"height: 15.0pt;\">\n<td height=\"20\" style=\"height: 15pt; text-align: center; width: 62px;\">{obj[2]}</td>\n<td style=\"padding-bottom: 4px; padding-top: 4px; width: 98px;\">{r1[2]}</td>\n<td style=\"padding-bottom: 4px; padding-top: 4px; width: 111px;\">{r2[2]}</td>\n</tr>\n<tr height=\"20\" style=\"height: 15.0pt;\">\n<td height=\"20\" style=\"height: 15pt; text-align: center; width: 62px;\">{obj[3]}</td>\n<td style=\"padding-bottom: 4px; padding-top: 4px; width: 98px;\">{r1[3]}</td>\n<td style=\"padding-bottom: 4px; padding-top: 4px; width: 111px;\">{r2[3]}</td>\n</tr>\n<tr height=\"20\" style=\"height: 15.0pt;\">\n<td height=\"20\" style=\"height: 15pt; text-align: center; width: 62px;\">{obj[4]}</td>\n<td style=\"padding-bottom: 4px; padding-top: 4px; width: 98px;\">{r1[4]}</td>\n<td style=\"padding-bottom: 4px; padding-top: 4px; width: 111px;\">{r2[4]}</td>\n</tr>\n<tr height=\"20\" style=\"height: 15.0pt;\">\n<td height=\"20\" style=\"height: 15pt; text-align: center; width: 62px;\">{obj[5]}</td>\n<td style=\"padding-bottom: 4px; padding-top: 4px; width: 98px;\">{r1[5]}</td>\n<td style=\"padding-bottom: 4px; padding-top: 4px; width: 111px;\">{r2[5]}</td>\n</tr>\n<tr height=\"20\" style=\"height: 15.0pt;\">\n<td height=\"20\" style=\"height: 15pt; text-align: center; width: 62px;\">{obj[6]}</td>\n<td style=\"padding-bottom: 4px; padding-top: 4px; width: 98px;\">{r1[6]}</td>\n<td style=\"padding-bottom: 4px; padding-top: 4px; width: 111px;\">{r2[6]}</td>\n</tr>\n<tr height=\"20\" style=\"height: 15.0pt;\">\n<td height=\"20\" style=\"height: 15pt; text-align: center; width: 62px;\">{obj[7]}</td>\n<td style=\"padding-bottom: 4px; padding-top: 4px; width: 98px;\">{r1[7]}</td>\n<td style=\"padding-bottom: 4px; padding-top: 4px; width: 111px;\">{r2[7]}</td>\n</tr>\n</tbody>\n</table>\n<div id=\"statement-input\" disabled=\"disabled\" data-bind=\"writemaths: statement, tinymce_plugins: ['jmevisible','preview'], variableReferrer: {value: statement, description: 'Statement', kind: 'html'}\">\n<p>Null hypothesis $H_0$: There is no association between the attitudes of wives and husbands.</p>\n</div>\n<p class=\"help-block\">Use statistics software to answer the following questions.</p>", "advice": "<p>Conduct a regression analysys using statistics software - e.g., in Minitab, use Stat | Regression | Fitted Line Plot.</p>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "extensions": ["stats"], "variables": {"rr1": {"name": "rr1", "group": "Ungrouped variables", "definition": "rk(r1)", "description": "", "templateType": "anything"}, "tol": {"name": "tol", "group": "Ungrouped variables", "definition": "0.05", "description": "", "templateType": "anything"}, "r1": {"name": "r1", "group": "Ungrouped variables", "definition": "darr(n,m,[random(1..20)])", "description": "", "templateType": "anything"}, "spxy": {"name": "spxy", "group": 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"", "templateType": "anything"}, "spcoef": {"name": "spcoef", "group": "Ungrouped variables", "definition": "precround(6*ssd/(n*(n^2-1)),3)", "description": "", "templateType": "anything"}, "ss": {"name": "ss", "group": "Ungrouped variables", "definition": "[ssq[0]-t[0]^2/n,ssq[1]-t[1]^2/n]", "description": "", "templateType": "anything"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "3", "description": "", "templateType": "anything"}, "v": {"name": "v", "group": "Ungrouped variables", "definition": "switch(corrcoef >=0.905,[4,0,0,0,0],corrcoef>=0.834,[0,4,0,0,0],corrcoef>=0.707,[0,0,4,0,0],corrcoef>=0.621,[0,0,0,4,0],[0,0,0,0,4])", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "8", "description": "", "templateType": "anything"}, "obj": {"name": "obj", "group": "Ungrouped variables", "definition": "['A','B','C','D','E','F','G','H']", "description": "", "templateType": "anything"}, "ssd": {"name": 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"sqrt(abs(l)/(abs(l)-1))*stdev(l)"}, "rk": {"parameters": [["a", "list"]], "type": "list", "language": "javascript", "definition": "/*This gives the ranking of the entries in a, c counts the ties */\n      var out = [];\n        for(var j=0;j<a.length;j++){\n      var s=0;\n      var c=0;\n      for(var i=0;i<a.length;i++){\n        if(a[j]>a[i]){s+=1;}\n        else\n      if(a[j]==a[i]){c+=1;}\n      }\n        out[j]=(2*s+c+1)/2;\n        }\n        return out;"}, "marr": {"parameters": [["a", "list"]], "type": "number", "language": "jme", "definition": "if(length(a)=2,max(a[0],a[1]),max(a[0],marr(a[1..length(a)])))"}}, "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>What are the parameters of&nbsp;the regression model $y = b_0 + b_1 \\times x$?</p>\n<p>$b_0=\\;$[[0]]</p>\n<p>$b_1=\\;$[[1]]</p>", "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": "b0*(1-tol)", "maxValue": "b0*(1+tol)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "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": "b1*(1-tol)", "maxValue": "b1*(1+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, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the correlation coefficient $R$, both as a decimal and as a percentage?</p>\n<p>$R=\\;$[[0]] $=\\;$[[1]]$\\%$</p>\n<p>&nbsp;</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": "0.5", "exploreObjective": null, "minValue": "corrcoef*(1-tol)", "maxValue": "corrcoef*(1+tol)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "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": "0.5", "exploreObjective": null, "minValue": "100*corrcoef*(1-tol)", "maxValue": "100*corrcoef*(1+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, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the R-squared coefficient, 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"extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "corrcoef", "part": "p1g0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": "0.5", "exploreObjective": null, "minValue": "100*rSquared*(1-tol)", "maxValue": "100*rSquared*(1+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, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Make a decision by choosing one of these options:</p>\n<p>[[0]]</p>\n<p></p>", "gaps": [{"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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 1, "showCellAnswerState": true, "choices": ["$p \\leq 0.002$, very strong evidence against $H_0$.", "$0.002 \\lt p \\leq 0.01$, strong evidence against $H_0$.", "$0.01 \\lt p \\leq 0.05$,&nbsp;some evidence against $H_0$.", "$0.05 \\lt p \\leq 0.1$, weak evidence against $H_0$ (do not reject $H_0$ but consider further investigation).", "$p 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