// Numbas version: exam_results_page_options
{"name": "20122013 CBA4_1", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"scripts": {}, "gaps": [{"showPrecisionHint": false, "scripts": {}, "allowFractions": false, "type": "numberentry", "correctAnswerFraction": false, "minValue": "p1", "showCorrectAnswer": true, "marks": 1, "maxValue": "p1"}], "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>$\\operatorname{P}(T \\lt \\var{v1})$ where $T \\sim t_{\\var{t}}$</p>\n        <p>$\\operatorname{P}(T \\lt \\var{v1})=\\;$?[[0]]</p>", "marks": 0}, {"scripts": {}, "gaps": [{"showPrecisionHint": false, "scripts": {}, "allowFractions": false, "type": "numberentry", "correctAnswerFraction": false, "minValue": "p2", "showCorrectAnswer": true, "marks": 1, "maxValue": "p2"}], "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>$\\operatorname{P}(T \\lt \\var{-v2})$ where $T \\sim t_{\\var{tn}}$</p>\n        <p>$\\operatorname{P}(T \\lt \\var{-v2})=\\;$ [[0]]</p>", "marks": 0}, {"scripts": {}, "gaps": [{"showPrecisionHint": false, "scripts": {}, "allowFractions": false, "type": "numberentry", "correctAnswerFraction": false, "minValue": "p3", "showCorrectAnswer": true, "marks": 1, "maxValue": "p3"}], "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>$\\operatorname{P}(T \\gt \\var{v3})$ where $T \\sim t_{\\var{tm}}$</p>\n        <p>$\\operatorname{P}(T \\gt \\var{v3})=\\;$?[[0]]</p>", "marks": 0}], "variables": {"u2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1..10 except u1)", "name": "u2", "description": ""}, "p1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "p[u1-1]", "name": "p1", "description": ""}, "p3": {"group": "Ungrouped variables", "templateType": "anything", "definition": "precround(1-p[u3-1],3)", "name": "p3", "description": ""}, "t": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(10..30)", "name": "t", "description": ""}, "per": {"group": "Ungrouped variables", "templateType": "anything", "definition": "['DF','0.75','0.800','0.850','0.900','0.950','0.975','0.990','0.995','0.999','0.9995']", "name": "per", "description": ""}, "p2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "precround(1-p[u2-1],3)", "name": "p2", "description": ""}, "u3": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1..10 except [u1,u2])", "name": "u3", "description": ""}, "v1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "cr(t)[u1]", "name": "v1", "description": ""}, "u1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1..10)", "name": "u1", "description": ""}, "tn": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(10..30 except t)", "name": "tn", "description": ""}, "p": {"group": "Ungrouped variables", "templateType": "anything", "definition": "[0.75,0.8,0.85,0.9,0.95,0.975,0.99,0.995,0.999,0.9995]", "name": "p", "description": ""}, "v2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "cr(tn)[u2]", "name": "v2", "description": ""}, "tm": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(10..30 except[t,tn])", "name": "tm", "description": ""}, "v3": {"group": "Ungrouped variables", "templateType": "anything", "definition": "cr(tm)[u3]", "name": "v3", "description": ""}}, "ungrouped_variables": ["p2", "p3", "p1", "v1", "u1", "per", "u2", "tn", "p", "v2", "tm", "t", "u3", "v3"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "20122013 CBA4_1", "functions": {"pc": {"type": "number", "language": "jme", "definition": "precround(studenttinv(p,n),3)", "parameters": [["p", "number"], ["n", "number"]]}, "cr": {"type": "list", "language": "jme", "definition": "[t,\n        pc(0.75,t),\n        pc(0.8,t),\n        pc(0.85,t),\n        pc(0.9,t),\n        pc(0.95,t),\n        pc(0.975,t),\n        pc(0.99,t),\n        pc(0.995,t),\n        pc(0.999,t),\n        pc(0.9995,t)\n        ]", "parameters": [["t", "number"]]}}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Use statistics tables or R to find the following:</p>\n    <p>&nbsp;</p>", "tags": ["MAS2302", "checked2015", "critical values", "one-sided", "statistics", "student", "student ", "t statistics", "t tables", "t test", "tables"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p><strong>27/01/2013:</strong></p>\n        <p>First draft completed.</p>", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Looking up t-tables.&nbsp;</p>"}, "advice": "<p>&nbsp;</p>\n    <p>a)</p>\n    <p>We have to find &nbsp;$\\operatorname{P}(T \\lt \\var{v1})$ where $T \\sim t_{\\var{t}}$.</p>\n    <p>Looking at the tables for degrees of freedom $\\var{t}$ ,</p>\n    <p>{table([cr(t)],per)} we see that the value $\\var{v1}$ &nbsp;corresponds to the $\\var{p1}$ critical point, and since the &nbsp;tables are one sided we see that $\\operatorname{P}(T \\lt \\var{v1})=\\var{p1}$&nbsp;</p>\n    <p>&nbsp;</p>\n    <p>&nbsp;b)</p>\n    <p>We have to find $\\operatorname{P}(T \\lt \\var{-v2})$ where $T \\sim t_{\\var{tn}}$. Looking at the table for degrees of freedom $\\var{tn}$ ,</p>\n    <p>{table([cr(tn)],per)} we see that since the tables are one sided,&nbsp;</p>\n    <p>$\\operatorname{P}(T \\lt \\var{-v2})=\\operatorname{P}(T \\gt \\var{v2})=1-\\operatorname{P}(T \\lt \\var{v2})=1-\\var{precround(1-p2,3)}=\\var{p2}$&nbsp;</p>\n    <p>&nbsp;c)</p>\n    <p>We have to find $\\operatorname{P}(T \\gt \\var{v3})$ where $T \\sim t_{\\var{tm}}$. Looking at the table for degrees of freedom $\\var{tm}$ ,</p>\n    <p>{table([cr(tm)],per)} we see that since the tables are one sided,&nbsp;</p>\n    <p>$\\operatorname{P}(T \\gt \\var{v3})=1-\\operatorname{P}(T \\lt \\var{v3})=1-\\var{precround(1-p3,3)}=\\var{p3}$&nbsp;</p>", "showQuestionGroupNames": false, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}