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Chapter 7: Q. 56 (page 479)
Making auto parts Refer to Exercise 54 . How many axles would you need to sample if you wanted the standard deviation of the sampling distribution of to be ? Justify your answer.
If the sample's standard deviation of the sampling distribution is , the sample should be 16 axles.
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On one episode of his show, a radio show host encouraged his listeners to visit his website and vote in a poll about proposed tax increases. Of the 4821 people who vote, 4277 are against the proposed increases. To which of the following populations should the results of this poll be generalized?
a. All people who have ever listened to this show
b. All people who listened to this episode of the show
c. All people who visited the show host's website
d. All people who voted in the poll
e. All people who voted against the proposed increases
What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the variability of the sampling distribution of the sample mean decreases." Is the student right? Explain your answer.
What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal." Is the student right? Explain your answer.
78 refer to the following setting. In the language of government statistics, you are "in the labor force" if you are available for work and either working or actively seeking work. The unemployment rate is the proportion of the labor force (not of the entire population) that is unemployed. Here are estimates from the Current Population Survey for the civilian population aged 25 years and over in a recent year. The table entries are counts in thousands of people.
Unemployment Suppose that you randomly select one person 25 years of age or older.
a. What is the probability that a randomly chosen person 25 years of age or older is in the labor force?
b. If you know that a randomly chosen person 25 years of age or older is a college graduate, what is the probability that he or she is in the labor force?
c. Are the events "in the labor force" and "college graduate" independent? Justify your answer.
Which of the following statements about the sampling distribution of the sample mean is incorrect?
a. The standard deviation of the sampling distribution will decrease as the sample size increases.
b. The standard deviation of the sampling distribution measures how far the sample mean typically varies from the population mean.
c. The sample mean is an unbiased estimator of the population mean.
d. The sampling distribution shows how the sample mean is distributed around the population mean.
e. The sampling distribution shows how the sample is distributed around the sample mean.
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