// Numbas version: exam_results_page_options
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You many assume that these data are normally distributed and the two groups have equal variance.</p>\n<p>{table_of_data}</p>\n<p>{download_link(\"two_tailed_t-test.csv\",csv)} to perform the calculations in your prefered statistical pacakage.</p>\n<!--<p>DEBUG</p>\n<p>mu_Y = {mu_Y}</p>\n<p>t_score = {t_score}</p>\n<p>p_value = {p_value}</p>-->", "advice": "<p>It is recommended that you use a statistical package to solve this question.</p>\n<p><a href=\"https://statisticsbyjim.com/hypothesis-testing/t-tests-excel/\">Here are instructions on how to conduct this test using Excel.</a></p>\n<p>If solving this question by hand you would use the following equation to workout the t score:</p>\n<p>\\[ T = \\frac{(\\bar{X}_1 -&nbsp;\\bar{X}_1) - (\\mu_1 - \\mu_2)}{S_c \\sqrt{1/n_1 + 1/n_2}}&nbsp; \\]</p>\n<p>Where \\(S_c\\) is the pooled standard deviation calculated by:</p>\n<p>\\[S_c^2 = \\frac{(n_1-1)S_1^2 +(n_2-1)S_2^2}{n_1 + n_2 -2} \\]</p>", "rulesets": {}, "extensions": ["download-text-file", "stats"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"X": {"name": "X", "group": "Ungrouped variables", "definition": "precround(vector(repeat(normalsample(0,1)+10,15)),3)", "description": "", "templateType": "anything", "can_override": false}, "mu_Y": {"name": "mu_Y", "group": "Ungrouped variables", "definition": "random(-1,-0.5,0,0.5,1)", "description": "", "templateType": "anything", "can_override": false}, "Y": {"name": "Y", "group": "Ungrouped variables", "definition": "precround(vector(repeat(normalsample(mu_y,1)+10,15)),3)", "description": "", "templateType": "anything", "can_override": false}, "d_bar": {"name": "d_bar", "group": "t score", "definition": "mean(difference)", "description": "", "templateType": "anything", "can_override": false}, "var_d": {"name": "var_d", "group": "t score", "definition": "variance(difference,true)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "t score", "definition": "len(list(X))", "description": "", "templateType": "anything", "can_override": false}, "t_score": {"name": "t_score", "group": "t score", "definition": "((d_bar)/(sqrt( (var_d/n) ) ))", "description": "", "templateType": "anything", "can_override": false}, "table_of_data": {"name": "table_of_data", "group": "Ungrouped variables", "definition": "table(zip(X,Y),[\"Group X\",\"Group Y\"])", "description": "", "templateType": "anything", "can_override": false}, "csv": {"name": "csv", "group": "Ungrouped variables", "definition": "csv(zip(X,Y),[\"X\",\"Y\"])", "description": "", "templateType": "anything", "can_override": false}, "p_value": {"name": "p_value", "group": "t score", "definition": "precround(ttest(t_score,(n -1),2),3)", "description": "<p>ttest return p value from t_score, degree of fredom and tails</p>", "templateType": "anything", "can_override": false}, "conclusion": {"name": "conclusion", "group": "Ungrouped variables", "definition": "if(p_value<0.05,\"reject\",\"not reject\")", "description": "<p>This in terms of the alternative hypothesis</p>", "templateType": "anything", "can_override": false}, "difference": {"name": "difference", "group": "t score", "definition": "X-Y", "description": "", "templateType": "anything", "can_override": false}, "neg_t_score": {"name": "neg_t_score", "group": "t score", "definition": "-1t_score", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "100"}, "ungrouped_variables": ["X", "mu_Y", "Y", "table_of_data", "csv", "conclusion"], "variable_groups": [{"name": "t score", "variables": ["t_score", "p_value", "n", "d_bar", "var_d", "difference", "neg_t_score"]}], "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>Calculate the absoulte value of the t score associated with the above hypothesis test.</p>\n<p>\\(|t|=\\) [[0]]</p>\n<p>Calculate the p value associated with the above hypothesis test.</p>\n<p>p = [[1]]</p>\n<p>Base on the above, there is evidence to&nbsp;[[2]] the null hypothesis. 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