// Numbas version: exam_results_page_options
{"name": "The t-distribution: application", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"p": {"templateType": "anything", "group": "Ungrouped variables", "definition": "siground(ttest(tStat,n,2),3)", "description": "", "name": "p"}, "tStat": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..3#0.01)", "description": "", "name": "tStat"}, "n": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(10..30)", "description": "", "name": "n"}, "CL": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(90,95,99)", "description": "", "name": "CL"}, "tol": {"templateType": "anything", "group": "Ungrouped variables", "definition": "0.05", "description": "", "name": "tol"}, "t": {"templateType": "anything", "group": "Ungrouped variables", "definition": "siground(-studenttinv(0.5*(100-CL)/100,n-1),3)", "description": "", "name": "t"}}, "statement": "<p>An independent random sample of size $n=\\var{n}$ is selected from an approximately normal population with unknown standard deviation.</p>", "ungrouped_variables": ["n", "CL", "t", "tol", "tStat", "p"], "parts": [{"extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "showFractionHint": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "prompt": "<p>What is the critical t-value ($t^\\star$) for a $\\var{CL}\\%$ confidence level?</p>", "showCorrectAnswer": true, "allowFractions": false, "marks": "5", "customName": "", "adaptiveMarkingPenalty": 0, "correctAnswerStyle": "plain", "type": "numberentry", "scripts": {}, "maxValue": "t*(1+tol)", "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "t*(1-tol)", "useCustomName": false}, {"extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "showFractionHint": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "prompt": "<p>Assuming a two-tailed test, what is the p-value for a test statistic $T=\\var{tStat}$?</p>", "showCorrectAnswer": true, "allowFractions": false, "marks": "5", "customName": "", "adaptiveMarkingPenalty": 0, "correctAnswerStyle": "plain", "type": "numberentry", "scripts": {}, "maxValue": "p*(1+tol)", "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "p*(1-tol)", "useCustomName": false}], "metadata": {"licence": "None specified", "description": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"js": "", "css": ""}, "rulesets": {}, "variable_groups": [], "name": "The t-distribution: application", "tags": [], "extensions": ["stats"], "advice": "<p>a) The number of degrees of freedom is $n-1$.</p>\n<p>An $x\\%$ confidence level corresponds to a two tails probability of $(100-x)\\%=(100-x)/100$.&nbsp;</p>\n<p>The critical value $t^\\star$ can now be obtained using statistical tables or software, e.g., the T.INV.2T Excel function.</p>\n<p>b) For a two-tailed test (which is the most common case), the $p$-value represents the probability in the tails of the $t$-distribution for a given test statistic, i.e., the proportion of the distribution falling more than $T$ units away from the mean.</p>\n<p>This can be obtained with software tools such as the T.DIST.2T Excel function.</p>", "functions": {}, "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/"}]}