// Numbas version: exam_results_page_options
{"name": "Charlie's copy of STAT7008 Hypothesis test, single sample, two sided t-test on sample mean", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"sample_mean_2": {"definition": "precround(mean(r1),2)", "name": "sample_mean_2", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "r1": {"definition": "repeat(round(normalsample(mu1,sigm1)),sample_size)", "name": "r1", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "mu1": {"definition": "random(72..75#0.5)", "name": "mu1", "description": "", "group": "Ungrouped variables", "templateType": "randrange"}, "sample_stdev_2": {"definition": "precround(sqrt(15*stdev(r1)^2/14),2)\n", "name": "sample_stdev_2", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "tcrit": {"definition": "precround(studenttinv(0.975,14),3)", "name": "tcrit", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "sigm1": {"definition": "random(5..8#0.5)", "name": "sigm1", "description": "", "group": "Ungrouped variables", "templateType": "randrange"}, "critical": {"definition": "if(sample_mean_2-mu0>0,tcrit,-tcrit)", "name": "critical", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "Falsec": {"definition": "if(test_statistic<1.96,\"There is sufficient evidence against the quoted percentage\",\n      \"There is insufficient evidence against the quoted percentage.\")", "name": "Falsec", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "mu0": {"definition": "mu1+k", "name": "mu0", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "Correctc": {"definition": "if(test_statistic>1.96,\"There is sufficient evidence against the quoted percentage.\",\n      \"There is insufficient evidence against the quoted percentage.\")", "name": "Correctc", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "mm": {"definition": "if(test_statistic<1.96,[0,1],[1,0])", "name": "mm", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "k": {"definition": "random(1..2.5#0.25)", "name": "k", "description": "", "group": "Ungrouped variables", "templateType": "randrange"}, "sample_size": {"definition": "15", "name": "sample_size", "description": "", "group": "Ungrouped variables", "templateType": "number"}, "test_statistic": {"definition": "precround((sample_mean_2-mu0)/(sample_stdev_2/sqrt(sample_size)),2)", "name": "test_statistic", "description": "", "group": "Ungrouped variables", "templateType": "anything"}}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>In this example we&nbsp;have a single sample of 15 data values. T</p>\n<p>\\(H_0:\\) The mean \\(=\\var{mu0}\\).</p>\n<p>\\(H_1:\\)&nbsp;The mean \\(\\ne \\var{mu0}\\).</p>\n<p>Given a sample of size \\(n\\) recall:</p>\n<p style=\"padding-left: 60px;\">the formula for the sample mean: &nbsp; &nbsp;\\(\\overline{x}=\\frac{\\sum {x}}{n}=\\var{sample_mean_2}\\)</p>\n<p style=\"padding-left: 60px;\">the formula for the sample standard deviation: &nbsp; \\(s=\\sqrt{\\frac{\\sum{(x-\\overline{x})^2}}{n-1}}=\\var{sample_stdev_2}\\)</p>\n<p style=\"padding-left: 60px;\">the formula for the t-statistic: &nbsp; \\(t=\\frac{\\overline{x}-\\mu}{\\frac{s}{\\sqrt{n}}}=\\frac{\\var{sample_mean_2}-\\var{mu0}}{\\frac{\\var{sample_stdev_2}}{\\sqrt{\\var{sample_size}}}}=\\var{test_statistic}\\)</p>\n<p>For a significance level of 5%:</p>\n<p>$t_{{\\frac{\\alpha}{2}},14}=\\var{critical}$</p>\n<p><strong><br/></strong>d)</p>\n<p>{Correctc}</p>", "tags": [], "parts": [{"unitTests": [], "sortAnswers": false, "variableReplacements": [], "showCorrectAnswer": true, "prompt": "<p><strong>Null Hypothesis</strong></p>\n<p>$\\operatorname{H}_0\\;: \\; \\mu=\\;$[[0]]</p>\n<p><strong>Alternative Hypothesis</strong></p>\n<p>$\\operatorname{H}_1\\;: \\; \\mu \\neq\\;$[[1]]</p>", "scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "marks": 0, "extendBaseMarkingAlgorithm": true, "gaps": [{"maxValue": "mu0", "unitTests": [], "variableReplacements": [], "correctAnswerFraction": false, "showCorrectAnswer": true, "correctAnswerStyle": "plain", "scripts": {}, "type": "numberentry", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "minValue": "mu0", "marks": 1, "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "showFeedbackIcon": true, "customMarkingAlgorithm": ""}, {"maxValue": "mu0", "unitTests": [], "variableReplacements": [], "correctAnswerFraction": false, "showCorrectAnswer": true, "correctAnswerStyle": "plain", "scripts": {}, "type": "numberentry", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "minValue": "mu0", "marks": 1, "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "showFeedbackIcon": true, "customMarkingAlgorithm": ""}], "showFeedbackIcon": true, "customMarkingAlgorithm": ""}, {"unitTests": [], "sortAnswers": false, "variableReplacements": [], "showCorrectAnswer": true, "prompt": "<p>Give all your answers correct to two decimal places.</p>\n<p>Input the sample mean:&nbsp; &nbsp;\\(\\bar{x}=\\) [[0]]</p>\n<p>Input the sample standard deviation:&nbsp; &nbsp;\\(s=\\) [[1]]</p>\n<p>Should we use the z or t test statistic? [[2]] enter z or t</p>\n<p>Enter the value for the test statistic:&nbsp; &nbsp;&nbsp;[[3]]</p>\n<p></p>", "scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "marks": 0, "extendBaseMarkingAlgorithm": true, "gaps": [{"precision": "2", "maxValue": "sample_mean_2", "precisionType": "dp", "unitTests": [], "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst", "minValue": "sample_mean_2", "marks": 1, "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "correctAnswerFraction": false, "variableReplacements": [], "showCorrectAnswer": true, "correctAnswerStyle": "plain", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "type": "numberentry", "allowFractions": false, "mustBeReducedPC": 0, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReduced": false, "customMarkingAlgorithm": ""}, {"precision": "2", "maxValue": "sample_stdev_2", 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1], "extendBaseMarkingAlgorithm": true, "checkingType": "absdiff", "showFeedbackIcon": true, "customMarkingAlgorithm": ""}, {"precision": "2", "maxValue": "test_statistic", "precisionType": "dp", "unitTests": [], "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst", "minValue": "test_statistic", "marks": "1", "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "correctAnswerFraction": false, "variableReplacements": [{"variable": "sample_mean_2", "part": "p0g0", "must_go_first": true}, {"variable": "sample_stdev_2", "part": "p0g1", "must_go_first": true}], "showCorrectAnswer": true, "correctAnswerStyle": "plain", "showPrecisionHint": false, "strictPrecision": false, "scripts": {}, "type": "numberentry", "allowFractions": false, "mustBeReducedPC": 0, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReduced": false, "customMarkingAlgorithm": ""}], "showFeedbackIcon": true, "customMarkingAlgorithm": ""}, {"unitTests": [], "sortAnswers": false, "variableReplacements": [], "showCorrectAnswer": true, "prompt": "<p>Use tables to find the critical value for a significance level of 5%.&nbsp;</p>\n<p></p>\n<p>critical value = [[0]]</p>\n<p></p>", "scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "marks": 0, "extendBaseMarkingAlgorithm": true, "gaps": [{"maxValue": "critical+0.01", "unitTests": [], "variableReplacements": [], "correctAnswerFraction": false, "showCorrectAnswer": true, "correctAnswerStyle": "plain", "scripts": {}, "type": "numberentry", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "minValue": "critical-0.01", "marks": 1, "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "showFeedbackIcon": true, "customMarkingAlgorithm": ""}], "showFeedbackIcon": true, "customMarkingAlgorithm": ""}, {"unitTests": [], "sortAnswers": false, "variableReplacements": [], "showCorrectAnswer": true, "prompt": "<p><strong>Your Decision: [[0]]</strong></p>\n<p><strong></strong></p>\n<p></p>\n<p><strong>&nbsp;</strong></p>\n<p><strong>Conclusion: [[1]]</strong></p>", "scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "marks": 0, "extendBaseMarkingAlgorithm": true, "gaps": [{"unitTests": [], "variableReplacements": [], "minMarks": 0, "choices": ["Reject", "Fail to reject"], "showCorrectAnswer": true, "shuffleChoices": false, "marks": 0, "type": "1_n_2", "displayColumns": 0, "showFeedbackIcon": true, "displayType": "radiogroup", "matrix": "mm", "showCellAnswerState": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "maxMarks": 0, "customMarkingAlgorithm": ""}, {"unitTests": [], "variableReplacements": [], "minMarks": 0, "choices": ["{Correctc}", "{Falsec}"], "showCorrectAnswer": true, "distractors": ["", ""], "shuffleChoices": false, "marks": 0, "type": "1_n_2", "displayColumns": 0, "showFeedbackIcon": true, "displayType": "radiogroup", "matrix": ["1", 0], "showCellAnswerState": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "maxMarks": 0, "customMarkingAlgorithm": ""}], "showFeedbackIcon": true, "customMarkingAlgorithm": ""}], "rulesets": {}, "name": "Charlie's copy of STAT7008 Hypothesis test, single sample, two sided t-test on sample mean", "extensions": ["stats"], "ungrouped_variables": ["sample_size", "r1", "sample_mean_2", "sample_stdev_2", "mu1", "sigm1", "k", "test_statistic", "mu0", "mm", "tcrit", "Correctc", "Falsec", "critical"], "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": ""}, "functions": {}, "statement": "<p>A sample of 15 deaths of men in Ireland during the past year was selected at random and the ages of each man at the time of death recorded. &nbsp;The data collected is presented below.</p>\n<table width=\"1185\" height=\"64\">\n<tbody>\n<tr>\n<td style=\"width: 63.5417px;\">{r1[0]}</td>\n<td style=\"width: 63.5417px;\">{r1[1]}</td>\n<td style=\"width: 63.5417px;\">{r1[2]}</td>\n<td style=\"width: 63.5417px;\">{r1[3]}</td>\n<td style=\"width: 63.5417px;\">{r1[4]}</td>\n<td style=\"width: 63.5417px;\">{r1[5]}</td>\n<td style=\"width: 63.5417px;\">{r1[6]}</td>\n<td style=\"width: 63.5417px;\">{r1[7]}</td>\n<td style=\"width: 63.5417px;\">{r1[8]}</td>\n<td style=\"width: 63.5417px;\">{r1[9]}</td>\n<td style=\"width: 63.5417px;\">{r1[10]}</td>\n<td style=\"width: 63.5417px;\">{r1[11]}</td>\n<td style=\"width: 63.5417px;\">{r1[12]}</td>\n<td style=\"width: 63.5417px;\">{r1[13]}</td>\n<td style=\"width: 63.5417px;\">{r1[14]}</td>\n</tr>\n</tbody>\n</table>\n<p>It is believed that the mean lifespan for Irish men is {mu0}&nbsp;&nbsp;years.</p>\n<p>Does the data support this theory?&nbsp;</p>\n<p></p>", "type": "question", "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}, {"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Charlie Earle", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3054/"}]}]}], "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}, {"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Charlie Earle", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3054/"}]}