CHAPTER 5 PROBABILISTIC FEATURES OF THE DISTRIBUTIONS OF CERTAIN SAMPLE STATISTICS Use these estimates as the mean / and standard deviation o for the respective U.S. populations, Suppose we select a simple random sample of size 50 independently from each population. What is the probability that the difference between sample means XB - XA will be more than 8? 5.4.2 In the study cited in Exercises 5.3.4 and 5.3.5, the calcium levels in men and women ages 60 years or older are summarized in the following table: Mean Standard Deviation Men 797 482 Women 660 414 Use these estimates as the mean / and standard deviation o for the U.S. populations for these age groups. If we take a random sample of 40 men and 35 women, what is the probability of obtaining a difference between sample means of 100 mg or more? 5.4.3 Given two normally distributed populations with equal means and variances of of = 100 and 02 = 80, what is the probability that samples of size n = 25 and n2 = 16 will yield a value of x1 - in greater than or equal to 8? 5.4.4 Given two normally distributed populations with equal means and variances of of = 240 and 05 = 350, what is the probability that samples of size n = 35 and n2 = 30 will yield a value of X1 - $2 as large as or larger than 10? 5.4.5 For a population of 17-year-old boys and 17-year-old girls, the means and standard deviations respectively, of their subscapular skinfold thickness values are as follows: boys, 9.7 and 6.0; girls, 15.6 and 9.5. Simple random samples of 40 boys and 35 girls are selected from the populations. What is the probability that the difference between sample means Xgirls - Xboys will be greater than 10? DISTRIBUTION OF THE