Chapter 5: Q13E (page 314)
Will the sampling distribution of always be approximately normally distributed? Explain
A sampling distribution is statistics derived by continuous sampling from a greater populace.
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Question: Refer to Exercise 5.3.
a. Find the sampling distribution of
b. Find the population variance
c. Show that is an unbiased estimator of .
d. Find the sampling distribution of the sample standard deviation .
e. Show that s is a biased estimator of
Cable TV subscriptions and “cord cutters.” According to a recent Pew Research Center Survey (December 2015), 15% of U.S. adults admitted they are “cord cutters,” i.e., they canceled the cable/satellite TV service they once subscribed to. (See Exercise 2.4, p. 72) In a random sample of 500 U.S. adults, let pn represent the proportion who are “cord cutters.”
a. Find the mean of the sampling distribution of .
b. Find the standard deviation of the sampling distribution of .
c. What does the Central Limit Theorem say about the shape of the sampling distribution of ?
d. Compute the probability that is less than .12.
e. Compute the probability that is greater than .10.
Refer to Exercise 5.5, in which we found the sampling distribution of the sample median. Is the median an unbiased estimator of the population mean m?
Purchasing decision. A building contractor has decided to purchase a load of the factory-reject aluminum siding as long as the average number of flaws per piece of siding in a sample of size 35 from the factory's reject pile is 2.1 or less. If it is known that the number of flaws per piece of siding in the factory's reject pile has a Poisson probability distribution with a mean of 2.5, find the approximate probability that the contractor will not purchase a load of siding
Length of job tenure. Researchers at the Terry College ofBusiness at the University of Georgia sampled 344 business students and asked them this question: “Over the course of your lifetime, what is the maximum number of years you expect to work for any one employer?” The sample resulted in x= 19.1 years. Assume that the sample of students was randomly selected from the 6,000 undergraduate students atthe Terry College and that = 6 years.
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