# Chapter 8

Chapter 8,

21. What is a sampling error? Could the value of the sampling error be zero? If it were 0, what would this mean? A sampling error is the difference between a sample statistic and its corresponding population parameter. Yes, if one were to determine the sum of these sampling errors over large numbers of samples the result would be very close to zero. This is true because the sample mean is an unbiased estimator of the population mean.

22. Lists the reasons for sampling. Give an example for each reason for sampling. 1. It would not be feasible or practical to contact an entire population. 2. It would be cost prohibitive to study an entire population.   3. It would be physically impossible to check all items in the population. 4. Due to the destructive nature of some tests. 5. Sample results are adequate.

34. Information from the American Institute of Insurance indicates the mean amount of life
insurance per household in the United States is \$110,000. This distribution follows the
normal distribution with a standard deviation of \$40,000.
a. If we select a random sample of 50 households, what is the standard error of the mean?= 40000/square root of 50=5656.85
b. What is the expected shape of the distribution of the sample mean?-normal
c. What is the likelihood of selecting a sample with a mean of at least \$112,000?= P(mean)=112000)=P(z>(112000-110000)/5656.85)=P(z>=.3536=1-P(z<.3536)=.3618
d. What is the likelihood of selecting a sample with a mean of more than \$100,000?= P(Mean > 100000) = P(z > (100000-110000)/5656.85)
= P(z>- 1.768) = 1 – P(z<- 1.768) = 0.9615
e. Find the likelihood of selecting a sample with a mean of more than \$100,000 but less
than \$112,000.= P(100000 < sample mean < 112000)
= P(sample mean > 100000) – P(sample mean >= 112000) = 0.9615 – 0.3618 = 0.5997.

Chapter 9 32,34,36

32. A state meat inspector in Iowa has been given the assignment of estimating the mean
net weight of...