// Numbas version: finer_feedback_settings
{"name": "Mitchum's copy of CI for a difference of means: embryonic stem cells", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Mitchum's copy of CI for a difference of means: embryonic stem cells", "tags": [], "metadata": {"description": "<p>Adapted from section 7.3.1 in <a href=\"https://www.openintro.org/book/os/\" target=\"_blank\">OpenIntro Statistics</a> (4th ed).</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>We are interested in whether treatment using embryonic stem cells (ESCs) improves heart function following a heart attack. The table below reports the change in heart pumping capacity (compared to pre attack, as percentage) for a group of subjects that received ESCs and for a control group. Subject assignment to the groups was random.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"width: 55px;\">ECS</td>\n<td style=\"width: 55px;\">control</td>\n</tr>\n<tr>\n<td style=\"width: 55px;\">{r1[0]}</td>\n<td style=\"width: 55px;\">{r2[0]}</td>\n</tr>\n<tr>\n<td style=\"width: 55px;\">{r1[1]}</td>\n<td style=\"width: 55px;\">{r2[1]}</td>\n</tr>\n<tr>\n<td style=\"width: 55px;\">{r1[2]}</td>\n<td style=\"width: 55px;\">{r2[2]}</td>\n</tr>\n<tr>\n<td style=\"width: 55px;\">{r1[3]}</td>\n<td style=\"width: 55px;\">{r2[3]}</td>\n</tr>\n<tr>\n<td style=\"width: 55px;\">{r1[4]}</td>\n<td style=\"width: 55px;\">{r2[4]}</td>\n</tr>\n<tr>\n<td style=\"width: 55px;\">{r1[5]}</td>\n<td style=\"width: 55px;\">{r2[5]}</td>\n</tr>\n<tr>\n<td style=\"width: 55px;\">{r1[6]}</td>\n<td style=\"width: 55px;\">{r2[6]}</td>\n</tr>\n<tr>\n<td style=\"width: 55px;\">{r1[7]}</td>\n<td style=\"width: 55px;\">{r2[7]}</td>\n</tr>\n<tr>\n<td style=\"width: 55px;\">{r1[8]}</td>\n<td style=\"width: 55px;\">{r2[8]}</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "advice": "<p>See section 7.3.1 in&nbsp;<a href=\"https://www.openintro.org/book/os/\" target=\"_blank\" rel=\"noopener noreferrer\">OpenIntro Statistics</a>.</p>", "rulesets": {}, "extensions": ["stats"], "variables": {"sd1": {"name": "sd1", "group": "Statistics", "definition": "stdev(r1,true)", "description": "", "templateType": "anything"}, "mean2": {"name": "mean2", "group": "Statistics", "definition": "mean(r2)", "description": "", "templateType": "anything"}, "tol": {"name": "tol", "group": "Setup", "definition": "0.05", "description": "", "templateType": "anything"}, "sigma1": {"name": "sigma1", "group": "Setup", "definition": "random(4.5..5.5#0.1)", "description": "", "templateType": "anything"}, "mu1": {"name": "mu1", "group": "Setup", "definition": "random(2.5..4.5#0.1)", "description": "<p>Population mean of sample 1.</p>", "templateType": "anything"}, "r2": {"name": "r2", "group": "Setup", "definition": "repeat(round(normalsample(mu2,sigma2)),n2)", "description": "", "templateType": "anything"}, "SE": {"name": "SE", "group": "Statistics", "definition": "siground(sqrt(sd1^2/n1+sd2^2/n2),3)", "description": "", "templateType": "anything"}, "sd2": {"name": "sd2", "group": "Statistics", "definition": "stdev(r2,true)", "description": "", "templateType": "anything"}, "mu2": {"name": "mu2", "group": "Setup", "definition": "random(-4.5..-2.5#0.1)", "description": "<p>Population mean of sample 2.</p>", "templateType": "anything"}, "n2": {"name": "n2", "group": "Setup", "definition": "9", "description": "", "templateType": "anything"}, "ciLower": {"name": "ciLower", "group": "Statistics", "definition": "siground(meanDiff-tStar*SE,3)", "description": "", "templateType": "anything"}, "mean1": {"name": "mean1", "group": "Statistics", "definition": "mean(r1)", "description": "", "templateType": "anything"}, "r1": {"name": "r1", "group": "Setup", "definition": "repeat(round(normalsample(mu1,sigma1)),n1)", "description": "", "templateType": "anything"}, "n1": {"name": "n1", "group": "Setup", "definition": "9", "description": "", "templateType": "anything"}, "sigma2": {"name": "sigma2", "group": "Setup", "definition": "random(2..3#0.1)", "description": "", "templateType": "anything"}, "tStar": {"name": "tStar", "group": "Statistics", "definition": "studenttinv(0.5*(100-CL)/100,n1-1)", "description": "", "templateType": "anything"}, "CL": {"name": "CL", "group": "Setup", "definition": "random(90,95,99)", "description": "<p>Confidence level.</p>", "templateType": "anything"}, "meanDiff": {"name": "meanDiff", "group": "Statistics", "definition": "siground(mean1-mean2,3)", "description": "", "templateType": "anything"}, "ciUpper": {"name": "ciUpper", "group": "Statistics", "definition": "siground(meanDiff+tStar*SE,3)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Setup", "variables": ["n1", "n2", "mu1", "mu2", "sigma1", "sigma2", "r1", "r2", "CL", "tol"]}, {"name": "Statistics", "variables": ["mean1", "mean2", "meanDiff", "SE", "sd1", "sd2", "tStar", "ciLower", "ciUpper"]}], "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>Calculate the following point estimate:</p>\n<p>$\\overline{x}_{ESC}-\\overline{x}_{control}=$ [[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "(meanDiff)*(1-tol)", "maxValue": "(meanDiff)*(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, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculating the standard error:</p>\n<p>$SE=$ [[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [{"variable": "sd1", "part": "p0g0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": "1", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "SE*(1-tol)", "maxValue": "SE*(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, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Calculate the $\\var{CL}\\%$ confidence interval for the mean difference in heart pumping capacity.</p>\n<p>Lower limit:&nbsp;[[0]]</p>\n<p>Upper limit:&nbsp;[[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "ciUpper*(1-tol)", "maxValue": "ciUpper*(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": "3", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "ciLower*(1-tol)", "maxValue": "ciLower*(1+tol)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "type": "question", "contributors": [{"name": "Mario Orsi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/427/"}, {"name": "Mitchum Bock", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5103/"}]}]}], "contributors": [{"name": "Mario Orsi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/427/"}, {"name": "Mitchum Bock", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5103/"}]}