// Numbas version: exam_results_page_options
{"name": "Confidence interval for the variance folic acid", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Confidence interval for the variance folic acid", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>The folic acid content ( g per 100g) of 8 samples of a particular brand of breakfast cereal are shown below:</p>\n<p></p>\n<table style=\"margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td>{d1}</td>\n<td>{d2}</td>\n<td>{d3}</td>\n<td>{d4}</td>\n<td>{d5}</td>\n<td>{d6}</td>\n<td>{d7}</td>\n<td>{d8}</td>\n</tr>\n</tbody>\n</table>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;</p>\n<p>The variance of the folic acid content samples was calculated to be $\\var{sample_var}$.</p>\n<p></p>\n<p>Calculate a 95% confidence interval for the variance of the folic acid content.</p>\n<p></p>", "advice": "<p>The $95$% confidence interval for the population variance $\\sigma^2$ is:</p>\n<p></p>\n<p>$a=\\frac{(n-1)\\times s^2}{\\chi^2_{upper,n-1}}=\\frac{(8-1)\\times \\var{s}^2}{\\chi^2_{0.975,7}}=\\var{lower}$</p>\n<p></p>\n<p>$b=\\frac{(n-1)\\times s^2}{\\chi^2_{lower,n-1}}=\\frac{(8-1)\\times \\var{s}^2}{\\chi^2_{0.025,7}}=\\var{upper}$</p>\n<p></p>\n<p></p>", "rulesets": {}, "extensions": ["stats"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"d1": {"name": "d1", "group": "Ungrouped variables", "definition": "random(160..179#1)", "description": "", "templateType": "anything", "can_override": false}, "d2": {"name": "d2", "group": "Ungrouped variables", "definition": "random(160..179#1)", "description": "", "templateType": "anything", "can_override": false}, "d3": {"name": "d3", "group": "Ungrouped variables", "definition": "random(160..179#1)", "description": "", "templateType": "anything", "can_override": false}, "d4": {"name": "d4", "group": "Ungrouped variables", "definition": "random(160..179#1)", "description": "", "templateType": "anything", "can_override": false}, "d5": {"name": "d5", "group": "Ungrouped variables", "definition": "random(160..179#1)", "description": "", "templateType": "anything", "can_override": false}, "d6": {"name": "d6", "group": "Ungrouped variables", "definition": "random(160..179#1)", "description": "<p>random(160..179#1)</p>", "templateType": "anything", "can_override": false}, "d7": {"name": "d7", "group": "Ungrouped variables", "definition": "random(160..179#1)", "description": "", "templateType": "anything", "can_override": false}, "d8": {"name": "d8", "group": "Ungrouped variables", "definition": "random(160..179#1)", "description": "", "templateType": "anything", "can_override": false}, "sample_var": {"name": "sample_var", "group": "Ungrouped variables", "definition": "precround(variance([d1,d2,d3,d4,d5,d6,d7,d8],true),3)", "description": "", "templateType": "anything", "can_override": false}, "chi_lower": {"name": "chi_lower", "group": "Ungrouped variables", "definition": " precround(chisquareinv(0.025,7),3)", "description": "", "templateType": "anything", "can_override": false}, "chi_upper": {"name": "chi_upper", "group": "Ungrouped variables", "definition": "precround(chisquareinv(0.975,7),3)", "description": "", "templateType": "anything", "can_override": false}, "lower": {"name": "lower", "group": "Ungrouped variables", "definition": "precround(sample_var*7/chi_upper,2)", "description": "", "templateType": "anything", "can_override": false}, "upper": {"name": "upper", "group": "Ungrouped variables", "definition": "precround(sample_var*7/chi_lower,2)", "description": "", "templateType": "anything", "can_override": false}, "s": {"name": "s", "group": "Ungrouped variables", "definition": "precround(sqrt(sample_var),4)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["d1", "d2", "d3", "d4", "d5", "d6", "d7", "d8", "sample_var", "chi_lower", "chi_upper", "lower", "upper", "s"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "d1", "part": "p1", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Please give your answers to two decimal places.</p>\n<p>What are the values of&nbsp; $\\chi^2_{{\\frac{\\alpha}{2},}{n-1}}$ and $\\chi^2_{1-{\\frac{\\alpha}{2},}{n-1}}$?</p>\n<p>$\\chi^2_{{\\frac{\\alpha}{2},}{n-1}}$ = [[0]]</p>\n<p>$\\chi^2_{1-{\\frac{\\alpha}{2},}{n-1}}$ = [[1]]</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": "chi_lower-0.01", "maxValue": "chi_lower+0.01", "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": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "chi_upper-0.01", "maxValue": "chi_upper+0.01", "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>Please give your answer to one decimal place.</p>\n<p>The&nbsp;lower limit is&nbsp;[[0]]</p>\n<p>The upper limit is&nbsp;[[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [{"variable": "chi_lower", "part": "p0g0", "must_go_first": false}, {"variable": "chi_upper", "part": "p0g1", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "lower-0.1", "maxValue": "lower+0.1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": 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": [{"variable": "chi_lower", "part": "p0g0", "must_go_first": false}, {"variable": "chi_upper", "part": "p0g1", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "upper-0.1", "maxValue": "upper+0.1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}]}]}], "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}]}