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homework_14_ans - MTH 1210 Biostatistics Apr 2809...

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MTH 1210 Biostatistics Apr 28’09 Homework #14 ( Hypothesis Testing for the Difference between Two Population Means ) See the handouts # 15, 15a, 15b. Use the MS Excel program Hypothesis_Testing_for_ the_Difference_between_Two_Population_Means.xls. Solving the problems remember that what we hope or expect to be able to conclude as a result of the hypothesis testing usually should be placed in the alternative hypothesis H A . Formulate at first the alternative hypothesis H A and then the null hypothesis H 0 which should be complementary to H A . Then, choose the proper sheet and block of cells in the aforementioned Excel program that correspond to your hypotheses H 0 and H A and enter the data only in the data entry cells belonging to the B - column. In the problems below assume that unknown population variances are equal . 7.3.1 (pg. 244 of the textbook) Subjects in a certain study included a sample of 40 men who claimed to engage in a variety of sports activities (multisport). The mean Body Mass Index (BMI) for these men was 22.41 with a standard deviation of 1.27 . A sample of 24 male rugby players had a mean BMI of 27.75 with a standard deviation of 2.64 . Is this sufficient evidence for one to clam that, in general, rugby players have a higher BMI than the multisport men? Let α = 0.01. SAMPLE 1 Size n 1 = 24 The mean x mean_1 * = 27.7 5 ONE-sided test Std. deviation s 1 = 2.64 HYPOTHESES SAMPLE 2 Size n 2 = 40 H 0 : µ 1 – µ 2 0 Null hypothesis The mean x mean_2 * = 22.4 1 Std. deviation s 2 = 1.27 H A : µ 1 – µ 2 > 0 Alternative hypothesis Hypothesized value of (µ 1 – µ 2 ) 0 = 0 df = n 1 + n 2 – 2 = 62 Level of significance α = 0.01 t (1 – α) = 2.3880 1 <== critical value at the upper right tail of the curve f(t) s p 2 = [(n 1 – 1)s 1 2 + (n 2 – 1)s 2 2 ]/(n 1 + n 2 – 2) = 3.60006 Test statistic t * = [(x mean_1 * – x mean_2 * ) – (µ 1 – µ 2 ) 0 ]/(s p 2 /n 1 + s p 2 /n 2 ) 1/2 = 10.9001 1
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REJECT H 0 BECAUSE t * = 10.9001 > 2.3880 1 = t (1 – α) {Students should follow their textbook pg. 235- and the Excel program Hypothesis_Testing_for_the_Difference_between_Two_Population_Means.xls, sheet 2, lowest block of cells} 7.3.7 (pg. 247 of the textbook) Cortisol level determinations were made on two samples of women at childbirth. Group 1 subjects underwent emergency cesarean section
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homework_14_ans - MTH 1210 Biostatistics Apr 2809...

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