// Numbas version: finer_feedback_settings
{"name": "Patrice's copy of Perform t-test for hypothesis given sample mean and standard deviation", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"prompt": "\n        <p><strong>Step 1: Null Hypothesis</strong></p>\n        <p>$\\operatorname{H}_0\\;: \\; \\mu=\\;$[[0]]</p>\n        <p><strong>Step 2: Alternative Hypothesis</strong></p>\n        <p>$\\operatorname{H}_1\\;: \\; \\mu \\neq\\;$[[1]]</p>\n        ", "gaps": [{"correctAnswerFraction": false, "allowFractions": false, "showPrecisionHint": false, "scripts": {}, "minValue": "thisamount", "showCorrectAnswer": true, "maxValue": "thisamount", "type": "numberentry", "marks": 0.5}, {"correctAnswerFraction": false, "allowFractions": false, "showPrecisionHint": false, "scripts": {}, "minValue": "thisamount", "showCorrectAnswer": true, "maxValue": "thisamount", "type": "numberentry", "marks": 0.5}], "marks": 0, "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "<p><strong>Step 3: Test statistic</strong></p>\n        <p>Should we use the z or t test statistic? [[0]] (enter z or t).</p>\n        <p>Now calculate the test statistic = ? [[1]] (to 3 decimal places)</p>", "gaps": [{"answer": "t", "vsetrange": [0, 1], "marks": 1, "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "checkvariablenames": false, "scripts": {}, "checkingtype": "absdiff", "showCorrectAnswer": true, "expectedvariablenames": [], "vsetrangepoints": 5}, {"correctAnswerFraction": false, "allowFractions": false, "showPrecisionHint": false, "scripts": {}, "minValue": "tval-tol", "showCorrectAnswer": true, "maxValue": "tval+tol", "type": "numberentry", "marks": 1}], "marks": 0, "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "\n        <p><strong>Step 4: p-value</strong></p>\n        <p>Use tables to find a range for your $p$-value.&nbsp;</p>\n        <p>Choose the correct range here for $p$ : [[0]]</p>\n        ", "gaps": [{"maxMarks": 0, "minMarks": 0, "marks": 0, "shuffleChoices": false, "distractors": ["", "", "", ""], "type": "1_n_2", "matrix": "mm", "choices": ["{pm[0]}", "{pm[1]}", "{pm[2]}", "{pm[3]}"], "displayType": "radiogroup", "scripts": {}, "showCorrectAnswer": true, "displayColumns": 0}], "marks": 0, "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "\n        <p><strong>Step 5: Conclusion</strong></p>\n        <p>&nbsp;</p>\n        <p>Given the $p$ - value and the range you have found, what is the strength of evidence against the null hypothesis?</p>\n        <p>[[0]]</p>\n        <p><strong>Your Decision:</strong></p>\n        <p>[[1]]</p>\n        <p><strong>&nbsp;</strong></p>\n        <p><strong>Conclusion:</strong></p>\n        <p>[[2]]</p>\n        ", "gaps": [{"maxMarks": 0, "minMarks": 0, "marks": 0, "shuffleChoices": false, "distractors": ["", "", "", ""], "type": "1_n_2", "matrix": "mm", "choices": ["{evi[0]}", "{evi[1]}", "{evi[2]}", "{evi[3]}"], "displayType": "radiogroup", "scripts": {}, "showCorrectAnswer": true, "displayColumns": 0}, {"maxMarks": 0, "minMarks": 0, "marks": 0, "shuffleChoices": false, "distractors": ["", ""], "type": "1_n_2", "matrix": "dmm", "choices": ["Retain", "Reject"], "displayType": "radiogroup", "scripts": {}, "showCorrectAnswer": true, "displayColumns": 0}, {"maxMarks": 0, "minMarks": 0, "marks": 0, "shuffleChoices": true, "distractors": ["", ""], "type": "1_n_2", "matrix": [1, 0], "choices": ["{Correctc}", "{Fac}"], "displayType": "radiogroup", "scripts": {}, "showCorrectAnswer": true, "displayColumns": 0}], "marks": 0, "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}], "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"things": {"name": "things", "description": "", "definition": "\"customers is taken.\"", "group": "Ungrouped variables", "templateType": "anything"}, "evi1": {"name": "evi1", "description": "", "definition": "[\"no\",\"slight\",\"moderate\",\"strong\"]", "group": "Ungrouped variables", "templateType": "anything"}, "here": {"name": "here", "description": "", "definition": "random(\"Barcelona\",\"Madrid\",\"Athens\",\"Berlin\",\"Palma\",\"Rome\",\"Paris\",\"Lisbon\")", "group": "Ungrouped variables", "templateType": "anything"}, "claim": {"name": "claim", "description": "", "definition": "\"The average cost of a flight with us to \"+ here + \" is just \u00a3\" + {thisamount} + \" (including all taxes and charges!)\"", "group": "Ungrouped variables", "templateType": "anything"}, "thisamount": {"name": "thisamount", "description": "", "definition": "random(70..90)", "group": "Ungrouped variables", "templateType": "anything"}, "m": {"name": "m", "description": "", "definition": "thisamount+random(1..15)", "group": "Ungrouped variables", "templateType": "anything"}, "evi": {"name": "evi", "description": "", "definition": "[\"None\",\"Slight\",\"Moderate\",\"Strong\"]", "group": "Ungrouped variables", "templateType": "anything"}, "resultis": {"name": "resultis", "description": "", "definition": "\"The mean cost of a flight to \"+ here + \" from this sample is \"", "group": "Ungrouped variables", "templateType": "anything"}, "tol": {"name": "tol", "description": "", "definition": "0.001", "group": "Ungrouped variables", "templateType": "anything"}, "fac": {"name": "fac", "description": "", "definition": "if(pval<2,\"There is sufficient evidence against the claim of the flight company\",\"There is insufficient evidence against the claim of the flight company.\")", "group": "Ungrouped variables", "templateType": "anything"}, "mm": {"name": "mm", "description": "", "definition": "switch(pval=0,[1,0,0,0],pval=1,[0,1,0,0],pval=2,[0,0,1,0],[0,0,0,1])", "group": "Ungrouped variables", "templateType": "anything"}, "correctc": {"name": "correctc", "description": "", "definition": "if(pval>1,\"There is sufficient evidence against the claim of the flight company.\",\"There is insufficient evidence against the claim of the flight company.\")", "group": "Ungrouped variables", "templateType": "anything"}, "this": {"name": "this", "description": "", "definition": "\"An online flight company makes the following claim:\"", "group": "Ungrouped variables", "templateType": "anything"}, "stand": {"name": "stand", "description": "", "definition": "random(15..25)", "group": "Ungrouped variables", "templateType": "anything"}, "confl": {"name": "confl", "description": "", "definition": "random(90,95,99)", "group": "Ungrouped variables", "templateType": "anything"}, "dothis": {"name": "dothis", "description": "", "definition": "switch(pval <2, 'retain','reject')", "group": "Ungrouped variables", "templateType": "anything"}, "tval1": {"name": "tval1", "description": "", "definition": "abs(m-thisamount)*sqrt(n)/stand", "group": "Ungrouped variables", "templateType": "anything"}, "tval": {"name": "tval", "description": "", "definition": "precround(tval1,3)", "group": "Ungrouped variables", "templateType": "anything"}, "pm": {"name": "pm", "description": "", "definition": "[\"is greater than 10%\",\"lies between 5% and 10%\",\"lies between 1% and 5%\",\"is less than 1%\"]", "group": "Ungrouped variables", "templateType": "anything"}, "crit": {"name": "crit", "description": "", "definition": "map(precround(x,3),x,[studenttinv((90+100)/200,n-1),studenttinv((95+100)/200,n-1),studenttinv((99+100)/200,n-1)])", "group": "Ungrouped variables", "templateType": "anything"}, "dmm": {"name": "dmm", "description": "", "definition": "if(pval<2,[1,0],[0,1])", "group": "Ungrouped variables", "templateType": "anything"}, "n": {"name": "n", "description": "", "definition": "random(10..30)", "group": "Ungrouped variables", "templateType": "anything"}, "test": {"name": "test", "description": "", "definition": "\"A rival flight company decides to test their claim.\"", "group": "Ungrouped variables", "templateType": "anything"}, "pval": {"name": "pval", "description": "", "definition": "switch(tval<crit[0],0,tval<crit[1],1,tval<crit[2],2,3)", "group": "Ungrouped variables", "templateType": "anything"}}, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "advice": "\n    <p>a)</p>\n  <p><strong>Step 1: Null Hypothesis</strong></p>\n  <p>$\\operatorname{H}_0\\;: \\; \\mu=\\;\\var{thisamount}$</p>\n  <p><strong>Step 2: Alternative Hypothesis</strong></p>\n  <p>$\\operatorname{H}_1\\;: \\; \\mu \\neq\\;\\var{thisamount}$</p>\n  <p>b)</p>\n  <p>We should use the t statistic as the population variance is unknown.</p>\n  <p>The test statistic:</p>\n  <p>\\[t =\\frac{ |\\var{m} -\\var{thisamount}|} {\\sqrt{\\frac{\\var{stand} ^ 2 }{\\var{n}}}} = \\var{tval}\\]</p>\n  <p>to 3 decimal places.</p>\n  <p>c)</p>\n  <p>As &nbsp;$n=\\var{n}$ we use the $t_{\\var{n-1}}$ tables. &nbsp;We have the following data from the tables:</p>\n  <p>{table([['Critical Value',crit[0],crit[1],crit[2]]],['p value','10%','5%','1%'])}</p>\n  <p>We see that the $p$ value {pm[pval]}<strong>.</strong></p>\n  <p><strong><br/></strong>d)</p>\n  <p>Hence there is {evi1[pval]} evidence against $\\operatorname{H}_0$ and so we {dothis}&nbsp;$\\operatorname{H}_0$.</p>\n  <p>{Correctc}</p>\n    ", "type": "question", "functions": {}, "showQuestionGroupNames": false, "statement": "\n    <p>{this}&nbsp;</p>\n    <p><em><strong>{claim}</strong></em></p>\n    <p>{test}</p>\n    <p>A sample of {n} {things}</p>\n    <p>{resultis} &pound;{m} with a standard &nbsp;deviation of &pound;{stand}.</p>\n    <p>Perform an appropriate hypothesis test to see if the claim made by the online flight company is substantiated (use a two-tailed test).</p>\n    ", "variable_groups": [], "tags": ["checked2015", "MAS1403"], "ungrouped_variables": ["claim", "pval", "evi1", "crit", "tval1", "things", "stand", "tol", "test", "pm", "correctc", "resultis", "here", "fac", "confl", "evi", "this", "dothis", "m", "dmm", "n", "mm", "thisamount", "tval"], "name": "Patrice's copy of Perform t-test for hypothesis given sample mean and standard deviation", "rulesets": {}, "metadata": {"notes": "\n        \t\t<p><strong>2/01/2012:</strong></p>\n        \t\t                <p>Added tag sc as has string variables in order to generate other scenarios.</p>\n        \t\t                <p>The jstat function&nbsp;studenttinv(critvalue,n-1) gives the critical p values correctly.</p>\n        \t\t                <p>Added tag diagram as the i-assess question advice has a nice graphic of the p-value and the appropriate decision.</p>\n        \t\t", "description": "<p>Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "contributors": [{"name": "Patrice Behan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1791/"}]}]}], "contributors": [{"name": "Patrice Behan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1791/"}]}