// Numbas version: exam_results_page_options
{"name": "Test istotno\u015bci dla dw\u00f3ch \u015brednich", "extensions": ["stats"], "custom_part_types": [], "resources": [["question-resources/Wzory.pdf", "/srv/numbas/media/question-resources/Wzory.pdf"], ["question-resources/t_Studenta.pdf", "/srv/numbas/media/question-resources/t_Studenta.pdf"], ["question-resources/Rozk\u0142ad_chi2.pdf", "/srv/numbas/media/question-resources/Rozk\u0142ad_chi2.pdf"], ["question-resources/Dystrybuanta_rozk\u0142adu_normalnego.pdf", "/srv/numbas/media/question-resources/Dystrybuanta_rozk\u0142adu_normalnego.pdf"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Test istotno\u015bci dla dw\u00f3ch \u015brednich", "tags": [], "metadata": {"description": "<p>Zadanie pozwala oceni\u0107 umiej\u0119tno\u015b\u0107 studenta w zakresie: formu\u0142owania hipotez, przeprowadzania testu istotno\u015bci, wnioskowania statystycznego.</p>\n<p>Zmienne losowe: dane surowe</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>Zastanawiamy si\u0119, czy wprowadzenie nowych przepis&oacute;w w zakresie pierwsze\u0144stwa pieszych spowodowa\u0142ozmian\u0119 udzia\u0142u procentowego kierowc&oacute;w zatrzymuj\u0105cych si\u0119 przed przej\u015bciem dla pieszych w celu przepuszczenia pieszego. Przeprowadzono badanie na 9 przej\u015bciach na tydzie\u0144 przed i tydzie\u0144 po zmianie przepis&oacute;w. Poni\u017csza tabela przedstawia procent kierowc&oacute;w zatrzymuj\u0105cych si\u0119 przed przej\u015bciem dla pieszych (w momencie, gdy pieszy oczekuje na przej\u015bcie) w celu przepuszczenia pieszego odpowiednio PRZED i PO wprowadzeniu nowych przepis&oacute;w. Na poziomie istotno\u015bci 0,05 zweryfikuj hipotez\u0119, \u017ce PRZED zmian\u0105 przepis&oacute;w procent kierowc&oacute;w ust\u0119puj\u0105cych pierwsze\u0144stwa pieszym by\u0142 ni\u017cszy ni\u017c PO wprowadzeniu przepis&oacute;w. Za\u0142&oacute;\u017c, \u017ce odchylenia standardowe obu populacji s\u0105 jednakowe (\ud835\udf0e<sub>1</sub>=\ud835\udf0e<sub>2</sub>).</p>\n<table style=\"height: 180px; width: 165px;\" border=\"1\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"width: 6px;\">\n<p>Nr przej\u015bcia</p>\n</td>\n<td style=\"width: 55px; height: 18px;\">\n<p>PRZED</p>\n<p>x<sub>i1</sub></p>\n</td>\n<td style=\"width: 55px; height: 18px;\">\n<p>PO</p>\n<p>x<sub>i2</sub></p>\n</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 6px;\">1</td>\n<td style=\"width: 55px; height: 18px;\">{r1[0]}</td>\n<td style=\"width: 55px; height: 18px;\">{r2[0]}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 6px;\">2</td>\n<td style=\"width: 55px; height: 18px;\">{r1[1]}</td>\n<td style=\"width: 55px; height: 18px;\">{r2[1]}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 6px;\">3</td>\n<td style=\"width: 55px; height: 18px;\">{r1[2]}</td>\n<td style=\"width: 55px; height: 18px;\">{r2[2]}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 6px;\">4</td>\n<td style=\"width: 55px; height: 18px;\">{r1[3]}</td>\n<td style=\"width: 55px; height: 18px;\">{r2[3]}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 6px;\">5</td>\n<td style=\"width: 55px; height: 18px;\">{r1[4]}</td>\n<td style=\"width: 55px; height: 18px;\">{r2[4]}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 6px;\">6</td>\n<td style=\"width: 55px; height: 18px;\">{r1[5]}</td>\n<td style=\"width: 55px; height: 18px;\">{r2[5]}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 6px;\">7</td>\n<td style=\"width: 55px; height: 18px;\">{r1[6]}</td>\n<td style=\"width: 55px; height: 18px;\">{r2[6]}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 6px;\">8</td>\n<td style=\"width: 55px; height: 18px;\">{r1[7]}</td>\n<td style=\"width: 55px; height: 18px;\">{r2[7]}</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"width: 6px;\">9</td>\n<td style=\"width: 55px; height: 18px;\">{r1[8]}</td>\n<td style=\"width: 55px; height: 18px;\">{r2[8]}</td>\n</tr>\n</tbody>\n</table>\n<p>Przyjmij, \u017ce:</p>\n<p>m<sub>1</sub> - \u015bredni procent kierowc&oacute;w PRZED zmian\u0105 przepis&oacute;w</p>\n<p>m<sub>2</sub> - \u015bredni procent kierowc&oacute;w PO zmianie przepis&oacute;w</p>", "advice": "", "rulesets": {}, "extensions": ["stats"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"sd1": {"name": "sd1", "group": "Statistics", "definition": "precround(stdev(r1,false),2)", "description": "", "templateType": "anything", "can_override": false}, "mean2": {"name": "mean2", "group": "Statistics", "definition": "precround(mean(r2),2)", "description": "", "templateType": "anything", "can_override": false}, "tol": {"name": "tol", "group": "Setup", "definition": "0.05", "description": "", "templateType": "anything", "can_override": false}, "sigma1": {"name": "sigma1", "group": "Setup", "definition": "random(4.5..5.5#0.1)", "description": "", "templateType": "anything", "can_override": false}, "mu1": {"name": "mu1", "group": "Setup", "definition": "random(20..50#1)", "description": "<p>Population mean of sample 1.</p>", "templateType": "anything", "can_override": false}, "r2": {"name": "r2", "group": "Setup", "definition": "repeat(round(normalsample(mu2,sigma2)),n2)", "description": "", "templateType": "anything", "can_override": false}, "SE": {"name": "SE", "group": "Statistics", "definition": "siground(sqrt(sd1^2/n1+sd2^2/n2),3)", "description": "", "templateType": "anything", "can_override": false}, "sd2": {"name": "sd2", "group": "Statistics", "definition": "precround(stdev(r2,false),2)", "description": "", "templateType": "anything", "can_override": false}, "mu2": {"name": "mu2", "group": "Setup", "definition": "random(30..70#1)", "description": "<p>Population mean of sample 2.</p>", "templateType": "anything", "can_override": false}, "n2": {"name": "n2", "group": "Setup", "definition": "9", "description": "", "templateType": "anything", "can_override": false}, "ciLower": {"name": "ciLower", "group": "Statistics", "definition": "siground(meanDiff-tStar*SE,3)", "description": "", "templateType": "anything", "can_override": false}, "mean1": {"name": "mean1", "group": "Statistics", "definition": "precround(mean(r1),2)", "description": "", "templateType": "anything", "can_override": false}, "r1": {"name": "r1", "group": "Setup", "definition": "repeat(round(normalsample(mu1,sigma1)),n1)", "description": "", "templateType": "anything", "can_override": false}, "n1": {"name": "n1", "group": "Setup", "definition": "9", "description": "", "templateType": "anything", "can_override": false}, "sigma2": {"name": "sigma2", "group": "Setup", "definition": "random(2..3#0.1)", "description": "", "templateType": "anything", "can_override": false}, "tStar": {"name": "tStar", "group": "Statistics", "definition": "studenttinv(0.5*(100-CL)/100,n1-1)", "description": "", "templateType": "anything", "can_override": false}, "CL": {"name": "CL", "group": "Setup", "definition": "random(90,95,99)", "description": "<p>Confidence level.</p>", "templateType": "anything", "can_override": false}, "meanDiff": {"name": "meanDiff", "group": "Statistics", "definition": "siground(mean1-mean2,3)", "description": "", "templateType": "anything", "can_override": false}, "ciUpper": {"name": "ciUpper", "group": "Statistics", "definition": "siground(meanDiff+tStar*SE,3)", "description": "", "templateType": "anything", "can_override": false}, "ttest2": {"name": "ttest2", "group": "Statistics", "definition": "((mean1-mean2)/sqrt(((n1*sd1^2+n2*sd2^2)*(1/n1+1/n2))/(n1+n2-2)))", "description": "<p>Warto\u015b\u0107 testu t dla dw&oacute;ch \u015brednich</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Setup", "variables": ["n1", "n2", "mu1", "mu2", "sigma1", "sigma2", "r1", "r2", "CL", "tol"]}, {"name": "Statistics", "variables": ["mean1", "mean2", "meanDiff", "SE", "sd1", "sd2", "tStar", "ciLower", "ciUpper", "ttest2"]}], "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>Formu\u0142owanie hipotezy. Wprowad\u017a odpowiedni znak (=, &lt;, &gt; lub !=). <em>Uwaga: ostatni znak przyj\u0119to na potrzeby kolokwium jako znak r&oacute;\u017cno\u015bci.</em></p>\n<p>H0: m<sub>1</sub> [[0]] m<sub>2</sub></p>\n<p>H1: m<sub>1</sub> [[1]] m<sub>2</sub></p>", "gaps": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "=", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "<", "displayAnswer": "", "matchMode": "regex"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [{"variable": "sd1", "part": "p2g0", "must_go_first": true}, {"variable": "sd2", "part": "p2g1", "must_go_first": true}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": "0.5", "exploreObjective": null, "prompt": "<p>Wiedz\u0105c, \u017ce:</p>\n<p>$\\overline{x}_{1}=${mean1}</p>\n<p>$\\overline{x}_{2}=${mean2}</p>\n<p>oraz</p>\n<p>${s_1}=${sd1}</p>\n<p>${s_2}=${sd2}</p>\n<p><strong>Oblicz warto\u015b\u0107 statystyki testowej</strong>:</p>\n<p>${t}=$ [[0]]</p>\n<p><strong>Wyznacz warto\u015b\u0107 krytyczn\u0105 </strong>(je\u017celi dotyczy, wprowad\u017a warto\u015b\u0107 z minusem):</p>\n<p>${t}_{\\alpha}=$ [[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ttest2*(1-tol)", "maxValue": "ttest2*(1+tol)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "-1.746", "maxValue": "-1.746", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain-eu"], "correctAnswerStyle": "plain-eu"}], "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>Wpisz ${1}$ przy prawid\u0142owej odpowiedzi oraz ${0}$ przy odpowiedzi nieprawid\u0142owej:</p>\n<p>[[0]] Nale\u017cy odrzuci\u0107 H0</p>\n<p>[[1]] Brakuje podstaw do odrzucenia H0</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "if(ttest2<-1.746,1,0)", "maxValue": "if(ttest2<-1.746,1,0)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "if(ttest2>-1.746,1,0)", "maxValue": "if(ttest2>-1.746,1,0)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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/"}, {"name": "Aleksandra Romanowska", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/11231/"}]}]}], "contributors": [{"name": "Mario Orsi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/427/"}, {"name": "Aleksandra Romanowska", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/11231/"}]}