DISTRIUTION OF THE SAMPLING MEAN
EXERCISES
5.3.1: The National Health and Nutrition Examination Survey of 1976-80 (A-1) found that the mean serum cholesterol level for U.S. male aged 20-74 years was 211. The standard deviation was approximately 90. Consider the sampling distribution of the sample mean based on samples of size 50 drawn from this population of males. What is the mean of the sampling distribution? The standard error?
ANSWER
211,12.7279
5.4.1: The following data on a serum cholesterol level in U.S. males:
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Population Age Mean Standard deviation
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A 20-24 180 43
B 25-34 199 49
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Suppose we select a simple random sample of size 50 independently from each population. What is the probability that the difference between sample mean will be more than 25?
ANSWER
0.2578
DISTRIBUTION OF THE SAMPLE PROPORTION
EXERCISE
5.5.1: A Survey by the National Center for Health Statistics (A-2) found that 33.2 percent of women 40 years of age and over had undergone a breast examination (BPE) within the previous year. If we select a simple random sample of size 200 from this population, what is the probability that the sample proportion of women who have had a BPE within the 0.37.
ANSWER
0.8135
DISTRIBUTION OF THE DIFFERENCE BETWEEN TWO SAMPLE PROPORTIONS
EXERCISE
5.6.1: In a certain population of retarded children, it is known that the proportion who are hyperactive is 0.40. A random sample of size 120 was drawn from this population, and a random sample of size 100 was drawn from another population or retarded children. If the proportion of hyperactive children is the same in both population, what is the probability that the sample would yield a difference, of p^1-p^2 , of 0.16 or more?
ANSWER
0.008