// Numbas version: exam_results_page_options
{"name": "Confidence interval - NHS satisfaction", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Confidence interval - NHS satisfaction", "tags": [], "metadata": {"description": "Assessing the ability to construct confidence intervals for proportions.", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>In a survey of $\\var{n}$ UK adults, $\\var{s}$ reported that they are satisfied with the national healthcare system (NHS).</p>", "advice": "<div id=\"questionDisplay\" data-bind=\"stopbinding: true\">\n<div class=\"question clearfix jme-scope\" data-bind=\"with: question, visible: question.isCurrentQuestion\" data-jme-context-description=\"Question 1\">\n<div class=\"adviceContainer\" data-bind=\"visible: adviceDisplayed\" localise-data-jme-context-description=\"question.advice\">\n<p>Check the learning material and/or the literature on confidence intervals (e.g., Chapter 5 in&nbsp;<a href=\"https://www.openintro.org/book/os/\" target=\"_blank\" rel=\"noopener noreferrer\">OpenIntro Statistics</a>).</p>\n</div>\n</div>\n</div>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"tol": {"name": "tol", "group": "Ungrouped variables", "definition": "0.03", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(100..999)", "description": "<p>Sample size.</p>", "templateType": "anything", "can_override": false}, "MoE_95": {"name": "MoE_95", "group": "Ungrouped variables", "definition": "siground(1.96*se,3)", "description": "", "templateType": "anything", "can_override": false}, "se": {"name": "se", "group": "Ungrouped variables", "definition": "siground(sqrt(p*(1-p)/n),3)", "description": "", "templateType": "anything", "can_override": false}, "CI95high": {"name": "CI95high", "group": "Ungrouped variables", "definition": "siground(100*(p+MoE_95),3)", "description": "", "templateType": "anything", "can_override": false}, "s": {"name": "s", "group": "Ungrouped variables", "definition": "round(n*random(0.2..0.8#0.1))", "description": "<p>\"Satisfied\" respondents.</p>", "templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "siground(s/n,3)", "description": "", "templateType": "anything", "can_override": false}, "CI95low": {"name": "CI95low", "group": "Ungrouped variables", "definition": "siground(100*(p-MoE_95),3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "s", "p", "tol", "se", "MoE_95", "CI95low", "CI95high"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the point estimate, both as a decimal and as a percentage:</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">decimal</td>\n<td style=\"text-align: center;\">percentage</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\hat{p}:$</td>\n<td style=\"text-align: center;\">[[0]]</td>\n<td style=\"text-align: center;\">[[1]]%</td>\n</tr>\n</tbody>\n</table>\n<p>&nbsp;</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "p*(1-tol)", "maxValue": "p*(1+tol)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "p", "part": "p0g0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "p*100*(1-tol)", "maxValue": "p*100*(1+tol)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Check the success-failure condition ($np\\ge10$ and $n(1-p)\\ge10$):</p>\n<ul>\n<li>$np\\approx$ [[0]]</li>\n<li>$n(1-p)\\approx$ [[1]]</li>\n</ul>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "p", "part": "p0g0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "n*p - 2", "maxValue": "n*p + 2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "p", "part": "p0g0", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "n*(1-p) - 2", "maxValue": "n*(1-p) + 2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the standard error of the sample proportion $\\hat{p}$?</p>", "minValue": "SE*(1-tol)", "maxValue": "SE*(1+tol)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "100", "precisionMessage": "", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the margin of error for the $95\\%$ confidence interval of $p$?</p>", "minValue": "MoE_95*(1-tol)", "maxValue": "MoE_95*(1+tol)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, 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