homework_10_ans

homework_10_ans - Course MTH 1210 May 1709...

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Course MTH 1210 May 17’09 Homework #10 ( answers ) ( Sampling Distribution of the Differences between Two Sample means ) Use handout #11 and MS Excel programs: Three_distributions.xls, sheet 3 , Sampling distribution of sample means and t distribution.xls, sheet 3 , and Confidence_Intervals_for_Difference_of_Means.xls , sheet 2 which are referred to below as PR1, PR2, PR3 respectively. 1. {example 6.4.3, pg. 176 Biostatistics} In the process of study of the effectiveness of an integrated outpatient dual-diagnosis treatment program for mentally ill subjects, it was found that among 18 subjects with schizophrenia, the mean number of treatment days was 4.7 with a standard deviation of 9.3 . For 10 subjects with bipolar disorder, the mean number of psychiatric disorder treatment days was 8.8 with a standard deviation of 11.5 . We wish to construct a 95% confidence interval for the difference between the means of the populations represented by these two samples. We assume that the two populations of number of psychiatric treatment days are approximately normally distributed, and the two population variances are equal ( in contrast to problem #4 in HW #9 ) With the program Confidence_Intervals_for_Difference_of_Means.xls , sheet 2 ( PR3 ) the solution can be obtained in the simplest way. Enter the relevant values in the corresponding cells: α = 0.05 B6 n 1 = 18 B8 n 2 = 10 D8 _ _ x 1 * = 4.7 B9 x 2 * = 8.8 D9 s 1 = 9.3 B10 s 2 = 11.5 D10 The program will compute and display all intermediate quantities and the confidence interval in question. But the solution can be found also without this program. _ _ Solution . It is given that n 1 = 18, x 1 * = 4.7, s 1 = 9.3 and n 2 = 10, x 2 * = 8.8, s 2 = 11.5; α = 0.05 . We’ll use the formula (11.6) to construct the confidence interval of interest. In order to determine the reliability factor t (1 – α/2) in (11.6) we use the program Sampling and t distributions.xls, sheet 3, for α = 0.05 and n 1 + n 2 – 2 = 18 + 10 – 2 = 26 degrees of

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homework_10_ans - Course MTH 1210 May 1709...

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