// Numbas version: finer_feedback_settings
{"name": "Simon's copy of Find z-score for sample and calculate confidence interval", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "name": "Simon's copy of Find z-score for sample and calculate confidence interval", "parts": [{"scripts": {}, "variableReplacements": [], "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "strictPrecision": false, "allowFractions": false, "customName": "", "mustBeReduced": false, "maxValue": "zscore", "marks": 2, "minValue": "zscore", "customMarkingAlgorithm": "", "showPrecisionHint": true, "showFeedbackIcon": true, "precisionType": "dp", "precision": "3", "type": "numberentry", 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"originalfirst", "useCustomName": false, "extendBaseMarkingAlgorithm": true, "prompt": "<p>Calculate the $95$% confidence interval for the population mean $\\mu$:</p>\n<p>Lower bound: [[0]]</p>\n<p>Upper bound: [[1]]</p>\n<p></p>\n<p></p>", "customMarkingAlgorithm": ""}], "functions": {}, "tags": [], "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["zscore", "lowerbound", "bottom", "this", "top", "upperbound", "samplemean", "these", "sstdev", "score", "samplesize", "expb", "expt"], "variablesTest": {"maxRuns": 100, "condition": ""}, "extensions": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "\n\t\t<p>Given mean and sd of 1000 sample returns on a scale of 1 to 7 together with a given score, find the z-score.</p>\n\t\t        <p>Also find the 95% confidence interval for the population mean.</p>\n\t\t"}, "advice": "<p><strong>(a) </strong></p>\n<p>The $z$-score is given by&nbsp;</p>\n<p>\\[z=\\frac{x- \\bar x}{\\sigma}=\\frac{\\var{score}-\\var{samplemean}}{\\var{sstdev}}=\\var{dpformat(zscore,3)}\\] (to 3 decimal places)</p>\n<p></p>\n<p></p>\n<p><strong>(b)</strong></p>\n<p>The 95% confidence interval for the mean is given by:</p>\n<p>$\\bar x \\pm z_{95\\%} \\frac{\\sigma}{\\sqrt{n}}$ where $z_{95 \\%} = 1.96$ for a two-sided confidence interval.</p>\n<p></p>\n<p>Hence, the lower bound for the 95% confidence interval is given by:</p>\n<p>Lower bound = $\\displaystyle \\var{samplemean}-1.96 \\times \\frac{ \\var{sstdev}}{\\sqrt{\\var{samplesize}}}=\\var{lowerbound}$</p>\n<p></p>\n<p>Upper bound = $\\displaystyle \\var{samplemean}+1.96 \\times \\frac{ \\var{sstdev}}{\\sqrt{\\var{samplesize}}}=\\var{upperbound}$</p>\n<p></p>\n<p>Hence for the population mean $\\mu$ &nbsp;we can say that $\\var{lowerbound} \\le\\mu \\le \\var{upperbound}$ with $95$% confidence.</p>", "statement": "\n\t<p>A recent survey asked $\\var{samplesize}$ {these} to rate {this} on a scale from $\\var{bottom}$ ({expb}) to $\\var{top}$ ({expt}).</p>\n\t    <p>The mean rating was $\\var{samplemean}$ with SD $\\var{sstdev}$.</p>\n\t    <p></p>\n\t    <p>Enter all values to 3 decimal places.</p>\n\t    <p></p>\n\t", "variables": {"lowerbound": {"definition": "precround(samplemean-1.96*sstdev/sqrt(samplesize),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "lowerbound", "description": ""}, "score": {"definition": "random(2..5#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "score", "description": ""}, "upperbound": {"definition": "precround(samplemean+1.96*sstdev/sqrt(samplesize),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "upperbound", "description": ""}, "samplemean": {"definition": "random(4.5..6.5#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "samplemean", "description": ""}, "bottom": {"definition": "1", "templateType": "anything", "group": "Ungrouped variables", "name": "bottom", "description": ""}, "this": {"definition": "'the importance of price when making food choice decisions'", "templateType": "anything", "group": "Ungrouped variables", "name": "this", "description": ""}, "zscore": {"definition": "precround((score-samplemean)/sstdev,3)", "templateType": "anything", "group": "Ungrouped variables", "name": "zscore", "description": ""}, "samplesize": {"definition": "1000", "templateType": "anything", "group": "Ungrouped variables", "name": "samplesize", "description": ""}, "top": {"definition": "7", "templateType": "anything", "group": "Ungrouped variables", "name": "top", "description": ""}, "these": {"definition": "'UK shoppers'", "templateType": "anything", "group": "Ungrouped variables", "name": "these", "description": ""}, "sstdev": {"definition": "random(0.9..2.0#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "sstdev", "description": ""}, "expt": {"definition": "'Extremely important'", "templateType": "anything", "group": "Ungrouped variables", "name": "expt", "description": ""}, "expb": {"definition": "'Not at all important'", "templateType": "anything", "group": "Ungrouped variables", "name": "expb", "description": ""}}, "variable_groups": [], "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/"}]}