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Chapter 6: Q 6E (page 339)

Explain what is meant by the statement, “We are 95% confident that an interval estimate contains μ.”

Short Answer

Expert verified

In economics, a confidence interval is an approximation of an interval that might include a population parameter. A set of numbers that is expected to encompass a population figure with a reasonable level of certainty.

Step by step solution

01

Step-by-Step Solution Step 1: Explanation

The statement expresses trust in the estimating method instead of on the specific interval determined from the data sample. It states that if this application is repeated numerous times using the identical approach, 95% of the resultant intervals will include μ.

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Most popular questions from this chapter

Unethical corporate conduct. How complicit are entrylevel accountants in carrying out an unethical request from their superiors? This was the question of interest in a study published in the journal Behavioral Research in Accounting (July 2015). A sample of 86 accounting graduate students participated in the study. After asking the subjects to perform what is clearly an unethical task (e.g., to bribe a customer), the researchers measured each subject’s intention to comply with the unethical request score. Scores ranged from -1.5 (intention to resist the unethical request) to 2.5 (intention to comply with the unethical request). Summary statistics on the 86 scores follow: x¯=2.42,s=2.84.

a. Estimate μ, the mean intention to comply score for the population of all entry-level accountants, using a 90% confidence interval.

b. Give a practical interpretation of the interval, part a.

c. Refer to part a. What proportion of all similarly constructed confidence intervals (in repeated sampling) will contain the true value of μ?

d. Compute the interval, x¯±2s. How does the interpretation of this interval differ from that of the confidence interval, part a?

USGA golf ball tests. The United States Golf Association (USGA) tests all new brands of golf balls to ensure that they meet USGA specifications. One test conducted is intended to measure the average distance traveled when the ball is hit by a machine called "Iron Byron," a name inspired by the swing of the famous golfer Byron Nelson. Suppose the USGA wishes to estimate the mean distance for a new brand to within 1 yard with 90% confidence. Assume that

past tests have indicated that the standard deviation of the distances Iron Byron hits golf balls is approximately 10 yards. How many golf balls should be hit by Iron Byron to achieve the desired accuracy in estimating the mean?

“Out of control” production processes. When companies employ control charts to monitor the quality of their products, a series of small samples is typically used to determine if the process is “in control” during the period of time in which each sample is selected. (We cover quality-control charts in Chapter 13.) Suppose a concrete-block manufacturer samples nine blocks per hour and tests the breaking strength of each. During 1 hour’s test, the mean and standard deviation are 985.6 pounds per square inch (psi) and 22.9 psi, respectively. The process is to be considered “out of control” if the true mean strength differs from 1,000 psi. The manufacturer wants to be reasonably certain that the process is really out of control before shutting down the process and trying to determine the problem. What is your recommendation?

If you use the Internet, haveyou ever paid to access or download music? This was oneof the questions of interest in a recent Pew Internet and American Life Project Survey (October ). Telephoneinterviews were conducted on a representative sample of adults living in the United States. For this sample, adults admitted that they have paid to download music.

a.Use the survey information to find a point estimatefor the true proportion of U.S. adults who have paid todownload music.

b.Find an interval estimate for the proportion, part a.Useconfidence interval.

c.Give a practical interpretation of the interval,part b.Your answer should begin with “We areconfident. . ..”

d.Explain the meaning of the phrase “confident.”

e.How many more adults need to be sampled to reducethe margin of error in the confidence interval by half?

Suppose N= 10,000, n= 2,000, and s= 50.

a. Compute the standard error of xusing the finite populationcorrection factor.

b. Repeat part a assuming n= 4,000.

c. Repeat part a assuming n= 10,000.

d. Compare parts a, b, and c and describe what happens to the standard error of xas nincreases.

e. The answer to part c is 0. This indicates that there is no sampling error in this case. Explain.
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