// Numbas version: exam_results_page_options {"name": "STAT7008 Hypothesis test given sample mean and population variance (vending machine)", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "STAT7008 Hypothesis test given sample mean and population variance (vending machine)", "tags": [], "metadata": {"description": "
Provided with information on a sample with sample mean and known population variance, use the z test to either or reject a given null hypothesis. One sided.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "{this} {stuff}
\n{claim}$\\var{thismuch}${units} and {var} {standarddev}.
\n{test}
\nTo investigate a sample of $\\var{n}$ {things} {resultis} $\\var{m}${units}.
\nPerform an appropriate hypothesis test to see if the claim made by the customers is substantiated. Assume a significance level of 5%.
", "advice": "a)
\nStep 1: Null Hypothesis
\n$\\operatorname{H}_0\\;: \\; \\mu=\\;\\var{thismuch}$
\nStep 2: Alternative Hypothesis
\n$\\operatorname{H}_1\\;: \\; \\mu \\lt\\;\\var{thismuch}$
\nb)
\nWe should use the z statistic as the population variance is known.
\nThe test statistic:
\n\\[z =\\frac{ \\var{m} -\\var{thismuch}} {\\frac{\\var{standarddev}}{\\sqrt{\\var{n}}}} = \\var{teststatistic}\\]
\nto 2 decimal places.
\nc)
\n\nFor a significance level of 5%:
\n$z_{{\\alpha}}=\\var{critical}$
\n
d)
We {dothis} $\\operatorname{H}_0$.
\n{Correctc}
", "rulesets": {}, "extensions": ["stats"], "variables": {"stand": {"name": "stand", "group": "Ungrouped variables", "definition": "random(15..25)", "description": "", "templateType": "anything"}, "thisvar": {"name": "thisvar", "group": "Ungrouped variables", "definition": "random(300..400#10)", "description": "", "templateType": "anything"}, "dothis": {"name": "dothis", "group": "Ungrouped variables", "definition": "switch(abs(teststatistic)$\\operatorname{H}_0\\;: \\; \\mu=\\;$[[0]]
\nStep 2: Alternative Hypothesis
\n$\\operatorname{H}_1\\;: \\; \\mu \\lt\\;$[[1]]
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\nShould we use the z or t test statistic? [[0]] (enter z or t).
\nNow calculate the test statistic = ? [[1]] (to 2 decimal places)
", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "z", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "z", "value": ""}]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "teststatistic-tol", "maxValue": "teststatistic+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": "The critical value is [[0]]
", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "minValue": "critical", "maxValue": "critical", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": 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": "Step 5:
\nYour Decision:
\n[[0]]
\n\n\n
Conclusion:
\n[[1]]
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