// Numbas version: exam_results_page_options
{"name": "Z-test on sample proportion", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Z-test on sample proportion", "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": ""}, "ungrouped_variables": ["Z95", "scenario", "decision_matrix", "Z99", "test_statistic", "Z90", "n1", "p", "prop1", "percentage", "pop_p"], "extensions": ["stats"], "type": "question", "statement": "<p>A recent poll of \\(\\var{n1}\\)&nbsp;people indicated that \\(\\var{prop1}\\) of them had delayed seeking healthcare treatment due to the associated cost.</p>\n<p>It has long been believed that \\(\\var{percentage}\\)% of people will delay seeking healthcare treatment due to the associated cost.&nbsp;</p>\n<p>Does the data support this theory?&nbsp;</p>\n<p></p>", "variable_groups": [], "functions": {}, "variables": {"Z99": {"name": "Z99", "templateType": "number", "description": "", "group": "Ungrouped variables", "definition": "2.58"}, "p": {"name": "p", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "precround({prop1}/{n1},2)"}, "Z95": {"name": "Z95", "templateType": "number", "description": "", "group": "Ungrouped variables", "definition": "1.96"}, "Z90": {"name": "Z90", "templateType": "number", "description": "", "group": "Ungrouped variables", "definition": "1.65"}, "test_statistic": {"name": "test_statistic", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "(p-percentage/100)/sqrt((percentage*(100-percentage)/10000)/n1)"}, "decision_matrix": {"name": "decision_matrix", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "[\n  [1,0,0,0],\n  [0,1,0,0],\n  [0,0,1,0],\n  [0,0,0,1]\n][scenario]"}, "n1": {"name": "n1", "templateType": "randrange", "description": "", "group": "Ungrouped variables", "definition": "random(360..450#10)"}, "percentage": {"name": "percentage", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "round(0.85*p*100)"}, "prop1": {"name": "prop1", "templateType": "randrange", "description": "", "group": "Ungrouped variables", "definition": "random(100..125#1)"}, "scenario": {"name": "scenario", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "sum(map(abs(test_statistic)<x,x,[Z90,Z95,Z99]))"}, "pop_p": {"name": "pop_p", "templateType": "anything", "description": "<p>pop_p</p>", "group": "Ungrouped variables", "definition": "precround({percentage}/100,2)"}}, "tags": [], "parts": [{"variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>Enter the value of the sample proportion: \\(p=\\) [[1]]</p>\n<p>Enter the value for the appropriate test statistic: Z =&nbsp;[[0]]</p>\n<p></p>", "scripts": {}, "showCorrectAnswer": true, "type": "gapfill", "gaps": [{"scripts": {}, "variableReplacements": [{"must_go_first": true, "part": "p0", "variable": "sample_mean_2"}, {"must_go_first": true, "part": "p0", "variable": "sample_stdev_2"}], "precisionPartialCredit": 0, "minValue": "test_statistic", "type": "numberentry", "maxValue": "test_statistic", "precision": "2", "mustBeReduced": false, "showPrecisionHint": true, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "showCorrectAnswer": true, "showFeedbackIcon": true, "strictPrecision": false, "precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "marks": "1"}, {"scripts": {}, "variableReplacements": [], "precisionPartialCredit": 0, "minValue": "{p}", "type": "numberentry", "maxValue": "{p}", "precision": "2", "mustBeReduced": false, "showPrecisionHint": true, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "showCorrectAnswer": true, "showFeedbackIcon": true, "strictPrecision": false, "precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "marks": 1}], "variableReplacementStrategy": "originalfirst", "marks": 0}, {"variableReplacements": [{"must_go_first": false, "part": "p0g0", "variable": "test_statistic"}], "matrix": "decision_matrix", "displayColumns": "1", "type": "1_n_2", "maxMarks": "2", "choices": ["<p>Reject the Null Hypothesis and conclude conclude that the proportion of people who will delay seeking healthcare treatment due to the associated cost is not given by \\(p=\\frac{\\var{percentage}}{100}\\).</p>", "<p>Reject the Null Hypothesis at the 5% significance level but accept the Null Hypothesis at the 1% significance level and conclude that the proportion of people who will delay seeking healthcare treatment due to the associated cost is given by \\(p=\\frac{\\var{percentage}}{100}\\).</p>", "<p>Reject the Null Hypothesis at the 10% significance level but accept the Null Hypothesis at the 5% significance level and conclude that the proportion of people who will delay seeking healthcare treatment due to the associated cost is given by \\(p=\\frac{\\var{percentage}}{100}\\).</p>", "<p>Accept the Null Hypothesis at the 10% significance level and conclude that the proportion of people who will delay seeking healthcare treatment due to the associated cost is given by \\(p=\\frac{\\var{percentage}}{100}\\).&nbsp;</p>"], "displayType": "radiogroup", "variableReplacementStrategy": "originalfirst", "shuffleChoices": false, "prompt": "<p>Having compared your test statistic with the table values for a two-tailed Z-test, select one&nbsp;of the following conclusions that best describes your conclusion.</p>", "minMarks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "marks": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "rulesets": {}, "advice": "<p></p>\n<p>\\(H_0:\\) &nbsp;p&nbsp;=\\(\\simplify{{percentage}/100}\\).</p>\n<p>\\(H_1:\\) p&nbsp;\\(\\ne \\simplify{{percentage}/100}\\).</p>\n<p>Given a sample of size \\(n\\) recall:</p>\n<p style=\"padding-left: 60px;\">the formula for the sample proportion:&nbsp; &nbsp; &nbsp; \\(\\overline{p}=\\frac{{x}}{n}\\) where \\(x\\) is the number of observations</p>\n<p style=\"padding-left: 360px;\">&nbsp;\\(\\overline{p}=\\frac{\\var{prop1}}{\\var{n1}}=\\var{p}\\)</p>\n<p style=\"padding-left: 60px;\">the formula for the Z-statistic:&nbsp; &nbsp; &nbsp;\\(Z=\\frac{\\overline{p}-p}{\\sqrt{\\frac{p(1-p)}{n}}}\\)</p>\n<p style=\"padding-left: 300px;\">\\(Z=\\frac{\\var{p}-\\var{pop_p}}{\\sqrt{\\frac{\\var{pop_p}(1-\\var{pop_p})}{\\var{n1}}}}\\)</p>\n<p style=\"padding-left: 300px;\">\\(Z=\\frac{\\simplify{{p}-{pop_p}}}{\\sqrt{\\simplify{{pop_p}*(1-{pop_p})/{n1}}}}=\\var{test_statistic}\\)</p>\n<p style=\"padding-left: 60px;\"></p>\n<p>The Z-table values will be for a two-tailed test are given below.&nbsp;</p>\n<p style=\"padding-left: 90px;\">significance&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 10%&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 5%&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1%</p>\n<p style=\"padding-left: 90px;\">&nbsp; &nbsp; &nbsp; limits&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; \\(\\pm1.65\\)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;\\(\\pm1.96\\)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;\\(\\pm2.58\\)</p>\n<p>Compare the test statistic with the Z-table values and choose your conclusion.</p>", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}