18. A population has a mean of 200 and a standard deviation of 50. A sample of size 100 will be taken and the sample meanwill be used to estimate the population mean.

a. What is the expected value of?

b. What is the standard deviation of?

c. Show the sampling distribution of.

d. What does the sampling distribution ofshow?

19. A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected andis used to estimate.

a. What is the probability that the sample mean will be within 5 of the population mean?

b. What is the probability that the sample mean will be within 10 of the population mean?

20. Assume the population standard deviation is ? = 25. Compute the standard error of the mean,for sample sizes of 50, 100, 150, and 200. What can you say about the size of the standard error of the mean as the sample size is increased?

21. Suppose a random sample of size 50 is selected from a population with ? = 10. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate).

a. The population size is infinite.

b. The population size is N = 50,000

c. The population size is N = 5000.

d. The population size is N = 500.

23. In the EAI sampling problem (see Figure 7.5), we showed that forn= 30, there was .5034 probability of obtaining a sample mean with$500 of the population mean.

a. What is the probability thatis within $500 of the population mean if a sample of size 60 is used?

b. Answer part (a) for a sample of size 120.

FIGURE 7.5PROBABILITY OF A SAMPLE MEAN BEING WITHIN $500 OF THE POPULATION MEAN for A SIMPLE RANDOM SAMPLE OF 30 EAI EMPLOYEES

Sampling distribution of T - =730.30 P(51,300 = X = 52,300) P(F