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{"name": "Simon's copy of 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": [{"extensions": ["stats"], "rulesets": {}, "metadata": {"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>"}, "variable_groups": [], "variables": {"tol": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "0.001", "name": "tol"}, "m": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "thismuch-random(2..8)", "name": "m"}, "fac": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "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.\")", "name": "fac"}, "zval1": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "(m-thismuch)*sqrt(n)/sqrt(thisvar)", "name": "zval1"}, "this": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "\"A vending machine fills cups with \"", "name": "this"}, "crit": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "[1.282,1.645,2.326]", "name": "crit"}, "test": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "\"Customers of the vending machine suspect the machine is under-filling.\"", "name": "test"}, "resultis": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": 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"templateType": "anything", "definition": "random(90,95,99)", "name": "confl"}}, "parts": [{"type": "gapfill", "marks": 0, "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      ", "gaps": [{"type": "numberentry", "marks": 0.5, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "mustBeReducedPC": 0, "maxValue": "thismuch", "scripts": {}, "customName": "", "variableReplacements": [], "correctAnswerFraction": false, "unitTests": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "useCustomName": false, "mustBeReduced": false, "showCorrectAnswer": true, "minValue": "thismuch", "showFractionHint": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}, {"type": "numberentry", "marks": 0.5, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "mustBeReducedPC": 0, "maxValue": "thismuch", "scripts": {}, "customName": "", "variableReplacements": [], "correctAnswerFraction": false, "unitTests": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "useCustomName": false, "mustBeReduced": false, "showCorrectAnswer": true, "minValue": "thismuch", "showFractionHint": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}], "scripts": {}, "customName": "", "variableReplacements": [], "unitTests": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "useCustomName": false, "sortAnswers": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}, {"type": "gapfill", "marks": 0, "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 =&nbsp;&nbsp;[[1]]&nbsp;</p>", "gaps": [{"type": "jme", "marks": 1, "checkVariableNames": false, "failureRate": 1, "valuegenerators": [{"value": "", "name": "z"}], "showPreview": true, "scripts": {}, "customName": "", "variableReplacements": [], "answer": "z", "vsetRangePoints": 5, "vsetRange": [0, 1], "unitTests": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "useCustomName": false, "showCorrectAnswer": true, "checkingAccuracy": 0.001, "checkingType": "absdiff", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}, {"marks": 1, "allowFractions": false, "precisionType": "dp", "mustBeReduced": false, "scripts": {}, "showCorrectAnswer": true, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": true, "type": "numberentry", "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "precision": "3", "mustBeReducedPC": 0, "extendBaseMarkingAlgorithm": true, "customName": "", "variableReplacements": [], "unitTests": [], "customMarkingAlgorithm": "", "useCustomName": false, "maxValue": "zval1", "minValue": "zval1", "correctAnswerFraction": false, "showFeedbackIcon": true}], "scripts": {}, "customName": "", "variableReplacements": [], "unitTests": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "useCustomName": false, "sortAnswers": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}, {"type": "gapfill", "marks": 0, "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      ", "gaps": [{"type": "1_n_2", "marks": 0, "minMarks": 0, "shuffleChoices": false, "scripts": {}, "customName": "", "variableReplacements": [], "showCellAnswerState": true, "unitTests": [], "customMarkingAlgorithm": "", "maxMarks": 0, "showFeedbackIcon": true, "useCustomName": false, "displayType": "radiogroup", "showCorrectAnswer": true, "matrix": "mm", "displayColumns": 0, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "choices": ["{pm[0]}", "{pm[1]}", "{pm[2]}", "{pm[3]}"]}], "scripts": {}, "customName": "", "variableReplacements": [], "unitTests": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "useCustomName": false, "sortAnswers": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}, {"type": "gapfill", "marks": 0, "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      ", "gaps": [{"type": "1_n_2", "marks": 0, "minMarks": 0, "shuffleChoices": false, "scripts": {}, "customName": "", "variableReplacements": [], "showCellAnswerState": true, "unitTests": [], "customMarkingAlgorithm": "", "maxMarks": 0, "showFeedbackIcon": true, "useCustomName": false, "displayType": "radiogroup", "showCorrectAnswer": true, "matrix": "mm", "displayColumns": 0, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "choices": ["{evi[0]}", "{evi[1]}", "{evi[2]}", "{evi[3]}"]}, {"type": "1_n_2", "marks": 0, "minMarks": 0, "shuffleChoices": false, "scripts": {}, "customName": "", "variableReplacements": [], "showCellAnswerState": true, "unitTests": [], "customMarkingAlgorithm": "", "maxMarks": 0, "showFeedbackIcon": true, "useCustomName": false, "displayType": "radiogroup", "showCorrectAnswer": true, "matrix": "dmm", "displayColumns": 0, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "choices": ["Retain", "Reject"]}, {"type": "1_n_2", "marks": 0, "minMarks": 0, "distractors": ["", ""], "shuffleChoices": true, "scripts": {}, "customName": "", "variableReplacements": [], "showCellAnswerState": true, "unitTests": [], "customMarkingAlgorithm": "", "maxMarks": 0, "showFeedbackIcon": true, "useCustomName": false, "displayType": "radiogroup", "showCorrectAnswer": true, "matrix": [1, 0], "displayColumns": 0, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "choices": ["{Correctc}", "{Fac}"]}], "scripts": {}, "customName": "", "variableReplacements": [], "unitTests": [], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "useCustomName": false, "sortAnswers": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "functions": {}, "name": "Simon's copy of Perform z-test for hypothesis given sample mean and population variance", "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  ", "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"], "advice": "<p><strong>(a)</strong></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></p>\n<p><strong>(b)</strong></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{dpformat(zval1,3)}\\]</p>\n<p>to 3 decimal places.</p>\n<p></p>\n<p><strong>(c)</strong></p>\n<p>Since we are carrying out a 1-tailed hypothesis test (we are testing specifically for <strong>under</strong>-filling) we must use the 1-tailed critical values for the normal distribution.</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/>(d)</strong></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>", "preamble": {"css": "", "js": ""}, "type": "question", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}