// Numbas version: exam_results_page_options
{"name": "Perform z-test for hypothesis given sample mean and population variance", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"tol": {"templateType": "anything", "group": "Ungrouped variables", "definition": "0.001", "description": "", "name": "tol"}, "dmm": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(pval<2,[1,0],[0,1])", "description": "", "name": "dmm"}, "confl": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(90,95,99)", "description": "", "name": "confl"}, "zval1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "abs(m-thismuch)*sqrt(n)/sqrt(thisvar)", "description": "", "name": "zval1"}, "pval": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(zval<crit[0],0,zval<crit[1],1,zval<crit[2],2,3)", "description": "", "name": "pval"}, "correctc": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(pval>1,\"There is sufficient evidence against the claim of the vending company.\",\n      \"There is insufficient evidence against the claim of the vending company.\")", "description": "", "name": "correctc"}, "crit": {"templateType": "anything", "group": "Ungrouped variables", "definition": "[1.282,1.645,2.326]", "description": "", "name": "crit"}, "this": {"templateType": "anything", "group": "Ungrouped variables", "definition": "\"A vending machine fills cups with \"", "description": "", "name": "this"}, "thismuch": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(140..160)", "description": "", "name": "thismuch"}, "n": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(50..100)", "description": "", "name": "n"}, "dothis": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(pval <2, 'retain','reject')", "description": "", "name": "dothis"}, "pm": {"templateType": "anything", "group": "Ungrouped variables", "definition": "[\"is greater than 10%\",\"lies between 5% and 10%\",\"lies between 1% and 5%\",\"is less than 1%\"]", "description": "", "name": "pm"}, "mm": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(pval=0,[1,0,0,0],pval=1,[0,1,0,0],pval=2,[0,0,1,0],[0,0,0,1])", "description": "", "name": "mm"}, "things": {"templateType": "anything", "group": "Ungrouped variables", "definition": "\"cups is taken\"", "description": "", "name": "things"}, "m": {"templateType": "anything", "group": "Ungrouped variables", "definition": "thismuch-random(3..15)", "description": "", "name": "m"}, "claim": {"templateType": "anything", "group": "Ungrouped variables", "definition": "\"The vending machine company claims each cup should be filled with \"", "description": "", "name": "claim"}, "evi1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "[\"no\",\"slight\",\"moderate\",\"strong\"]", "description": "", "name": "evi1"}, "units": {"templateType": "anything", "group": "Ungrouped variables", "definition": "'ml'", "description": "", "name": "units"}, "zval": {"templateType": "anything", "group": "Ungrouped variables", "definition": "precround(zval1,3)", "description": "", "name": "zval"}, "test": {"templateType": "anything", "group": "Ungrouped variables", "definition": "\"Customers of the vending machine suspect the machine is under-filling.\"", "description": "", "name": "test"}, "fac": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(pval<2,\"There is sufficient evidence against the claim of the vending company\",\n      \"There is insufficient evidence against the claim of the vending company.\")", "description": "", "name": "fac"}, "var": {"templateType": "anything", "group": "Ungrouped variables", "definition": "\"the variance of the filling process is known to be \"", "description": "", "name": "var"}, "thisvar": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(300..500#10)", "description": "", "name": "thisvar"}, "evi": {"templateType": "anything", "group": "Ungrouped variables", "definition": "[\"None\",\"Slight\",\"Moderate\",\"Strong\"]", "description": "", "name": "evi"}, "stand": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(15..25)", "description": "", "name": "stand"}, "resultis": {"templateType": "anything", "group": "Ungrouped variables", "definition": "\"giving a mean of \"", "description": "", "name": "resultis"}}, "ungrouped_variables": ["claim", "var", "pval", "evi1", "crit", "zval1", "things", "tol", "units", "thismuch", "pm", "correctc", "resultis", "thisvar", "test", "zval", "fac", "confl", "evi", "mm", "dothis", "m", "dmm", "n", "this", "stand"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Perform z-test for hypothesis given sample mean and population variance", "functions": {}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "thismuch", "minValue": "thismuch", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "thismuch", "minValue": "thismuch", "correctAnswerFraction": false, "marks": 0.5, "showPrecisionHint": false}], "type": "gapfill", "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>$\\operatorname{H}_1\\;: \\; \\mu \\lt\\;$[[1]]</p>\n      ", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"answer": "z", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "showCorrectAnswer": true, "marks": 1, "vsetrangepoints": 5}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "zval+tol", "minValue": "zval-tol", "correctAnswerFraction": false, "marks": 1, "showPrecisionHint": false}], "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>", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"displayType": "radiogroup", "choices": ["{pm[0]}", "{pm[1]}", "{pm[2]}", "{pm[3]}"], "displayColumns": 0, "distractors": ["", "", "", ""], "shuffleChoices": false, "scripts": {}, "minMarks": 0, "type": "1_n_2", "maxMarks": 0, "showCorrectAnswer": true, "matrix": "mm", "marks": 0}], "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        \n      ", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"displayType": "radiogroup", "choices": ["{evi[0]}", "{evi[1]}", "{evi[2]}", "{evi[3]}"], "displayColumns": 0, "distractors": ["", "", "", ""], "shuffleChoices": false, "scripts": {}, "minMarks": 0, "type": "1_n_2", "maxMarks": 0, "showCorrectAnswer": true, "matrix": "mm", "marks": 0}, {"displayType": "radiogroup", "choices": ["Retain", "Reject"], "displayColumns": 0, "distractors": ["", ""], "shuffleChoices": false, "scripts": {}, "minMarks": 0, "type": "1_n_2", "maxMarks": 0, "showCorrectAnswer": true, "matrix": "dmm", "marks": 0}, {"displayType": "radiogroup", "choices": ["{Correctc}", "{Fac}"], "displayColumns": 0, "distractors": ["", ""], "shuffleChoices": true, "scripts": {}, "minMarks": 0, "type": "1_n_2", "maxMarks": 0, "showCorrectAnswer": true, "matrix": [1, 0], "marks": 0}], "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        \n      ", "showCorrectAnswer": true, "marks": 0}], "statement": "\n  <p>{this} {stuff}</p>\n    <p>{claim}$\\var{thismuch}${units} and {var} {thisvar}.</p>\n    <p>{test}</p>\n    <p>To investigate a sample of $\\var{n}$ {things} {resultis} $\\var{m}${units}.&nbsp;</p>\n    <p>Perform an appropriate hypothesis test to see if the claim made by the customers is substantiated.</p>\n  ", "tags": ["checked2015", "MAS1403"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "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>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", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Provided with information on a sample with sample mean and known population variance, use the z test to either accept or reject a given null hypothesis.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "\n  <p>a)</p>\n    <p><strong>Step 1: Null Hypothesis</strong></p>\n    <p>$\\operatorname{H}_0\\;: \\; \\mu=\\;\\var{thismuch}$</p>\n    <p><strong>Step 2: Alternative Hypothesis</strong></p>\n    <p>$\\operatorname{H}_1\\;: \\; \\mu \\lt\\;\\var{thismuch}$</p>\n    <p>b)</p>\n    <p>We should use the z statistic as the population variance is known.</p>\n    <p>The test statistic:</p>\n    <p>\\[z =\\frac{ |\\var{m} -\\var{thismuch}|} {\\sqrt{\\frac{\\var{thisvar}}{\\var{n}}}} = \\var{zval}\\]</p>\n    <p>to 3 decimal places.</p>\n    <p>c)</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  ", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}