// Numbas version: exam_results_page_options
{"name": "Sample mean, standard deviation and standard error", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Sample mean, standard deviation and standard error", "tags": [], "metadata": {"description": "<p>Compute a 95% confidence interval for the population mean given a small sample, and compare it with a confidence interval for a different population.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>The amount of sugar in a particular brand of breakfast cereal is to be determined. $\\var {num_monday}$ replicate samples weighing 10 grams were selected at random and the amount of sugar (grams) measured for each replicate is shown in the table below.</p>\n<p>{table([['Sugar (g)']+mon],[])}</p>", "advice": "<h4>a)</h4>\n<p>The mean of the sample is:&nbsp;</p>\n<p>\\[ \\bar{x} = \\frac{1}{n}(\\sum x_i) = \\var{precround(monday_mean,2)} \\text{ (to 2 d.p.)} \\]</p>\n<p>The standard deviation is:</p>\n<p>\\[ s = \\sqrt{\\frac{1}{n-1}\\sum \\left(x_i-\\bar{x}\\right)^2} = \\var{precround(monday_sd,2)} \\text{ (to 2 d.p.)} \\]</p>\n<p>The standard error is :</p>\n<p></p>\n<p>$\\frac{s}{\\sqrt {n}}=\\frac{\\var{precround(monday_sd,2)}}{\\sqrt{\\var{num_monday}}}=\\var{precround(monday_se,2)}$&nbsp;</p>\n<h4></h4>", "rulesets": {}, "extensions": ["stats"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"mon": {"name": "mon", "group": "Ungrouped variables", "definition": "repeat(pop_mean+random(0.1..0.8#0.1),num_monday)", "description": "<p>Data for Monday</p>", "templateType": "anything", "can_override": false}, "monday_mean": {"name": "monday_mean", "group": "Ungrouped variables", "definition": "mean(mon)", "description": "", "templateType": "anything", "can_override": false}, "num_monday": {"name": "num_monday", "group": "Ungrouped variables", "definition": "random(8..15#1)", "description": "", "templateType": "anything", "can_override": false}, "monday_sd": {"name": "monday_sd", "group": "Ungrouped variables", "definition": "stdev(mon, true)", "description": "", "templateType": "anything", "can_override": false}, "monday_se": {"name": "monday_se", "group": "Ungrouped variables", "definition": "monday_sd/sqrt(num_monday)", "description": "", "templateType": "anything", "can_override": false}, "pop_mean": {"name": "pop_mean", "group": "Ungrouped variables", "definition": "random(0.5..2.5#0.1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["num_monday", "mon", "monday_mean", "monday_sd", "monday_se", "pop_mean"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", 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