homework_9_ans

# homework_9_ans - Course MTH 1210 May 1709...

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Course MTH 1210 May 17’09 Homework #9 ( 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. {problem 5.4.3, pg. 145 Biostatistics} Given two normally distributed populations with equal means and variances of σ 1 2 = 100 and σ 2 2 = 80 , what is a probability that samples of size n 1 = 25 and n 2 = 16 will yield a value of x mean_1 – x mean_2 greater than or equal to 8 ? Solution . From the formula (11.2) we obtain _______________ _______________ σ x_mean_1 – x_mean_2 = √(σ 1 2 /n 1 ) + (σ 2 2 /n 2 ) = √(100/25) + (80/16) = 3 Now we run the program Three_distributions.xls, sheet 3 , enter the given value of difference x mean_1 – x mean_2 of two sample means ( 8 ) in the cell G57 (for x ), the value of 0 (the difference between two population means) in the cell G58 (for µ ), and the value of standard error of 3 in the cell G59 (for σ ), and get the probability we are seeking for in the cell I60 : P(X ≥ x) = 1 – f(X ≤ x) = 1 – 0.99617 = 0.00383 . 2. {problem 5.4.5, pg. 145 Biostatistics} For the population 1 of 17-year-old girls and population 2 of 17-year-old boys the means and the standard deviations, respectively, of their subscapular skinfold thickness values are as follows: girls, 15.6 and 9.5 ; boys, 9.7 and 6.0 . Simple random samples of 35 girls and 40 boys are selected from the populations. What is a probability that the difference between sample means

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homework_9_ans - Course MTH 1210 May 1709...

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