// Numbas version: exam_results_page_options
{"name": "Confidence intervals - fill in the gaps", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Confidence intervals - fill in the gaps", "tags": [], "metadata": {"description": "<p>Assessment of basic knowledge of confidence intervals; no randomisation.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>Fill in the gaps in the following sentences regarding confidence intervals.</p>", "advice": "<p>Revise confidence intervals, e.g., Sections 5.2 and 7.1 of&nbsp;<a href=\"https://leanpub.com/openintro-statistics\">OpenIntro Statistics</a>&nbsp;(4th edition).</p>\n<p>a) A CI aims at providing a \"guess\" (in the form of an interval) for a <em>population</em> (note that we don't need to guess a sample mean, we know exactly what it is, whereas we normally don't know a population mean, and that's why we need to guess).</p>\n<p>b) A CI for the population mean ($\\mu$) is built around the best available estimate for $\\mu$, which is the sample <em>mean</em>.</p>\n<p>c) The most common/conventional CI is the $95\\%$ CI (which also corresponds to the most common significance level&nbsp;$\\alpha=5\\%$).</p>\n<p>d) As a CI is defined as either $\\pm z^*\\times SE$ or&nbsp;$\\pm t^*\\times SE$, the larger SE the <em>larger</em> the CI.</p>\n<p>e) Considering d) above, and noting that $SE$ is defined as either $\\sqrt{\\frac{p(1-p)}{n}}$ (for a proportion) or $\\frac{SD}{\\sqrt{n}}$ (for numerical data), a larger sample size $n$ will result in a <em>smaller</em> CI.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "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>A confidence interval&nbsp;represents a range of values within which we are likely (but not certain) to find a&nbsp;[[0]]parameter.</p>\n<p><em>Hint: input one of \"categorical\", \"population\", \"sample\".</em></p>", "gaps": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "population", "displayAnswer": "population", "matchMode": "regex"}], "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>A confidence interval for $\\mu$ is always centered around the sample [[0]].</p>\n<p><em>Hint: input the name (not the symbol) of a common statistical quantity (a point estimate).</em></p>", "gaps": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "mean|average", "displayAnswer": "mean or average", "matchMode": "regex"}], "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>The most common confidence level is [[0]]%.</p>\n<p><em>Hint: input an integer (a whole number).</em></p>", "gaps": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "95", "displayAnswer": "95", "matchMode": "exact"}], "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>All else being equal, a larger standard error results in a confidence interval that is [[0]].</p>\n<p><em>Hint: input one of \"larger\", \"smaller\" or \"unchanged\".</em></p>", "gaps": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "larger", "displayAnswer": "larger", "matchMode": "exact"}], "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>All else being equal, a larger sample size results in a confidence interval that is [[0]].</p>\n<p><em>Hint: input one of \"larger\", \"smaller\" or \"unchanged\".</em></p>", "gaps": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "smaller", "displayAnswer": "smaller", "matchMode": "exact"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Mario Orsi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/427/"}]}]}], "contributors": [{"name": "Mario Orsi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/427/"}]}