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Chapter 10: Problem 87

A random sample of \(n=44\) individuals with a B.S. degree in accounting who started with a Big Eight accounting firm and subsequently changed jobs resulted in a sample mean time to change of \(35.02\) months and a sample standard deviation of \(18.94\) months ("The Debate over Post-Baccalaureate Education: One University's Experience," Issues in Accounting Education [1992]: 18-36). Can it be concluded that the true average time to change exceeds 2 years? Test the appropriate hypotheses using a significance level of \(.01\).

Short Answer

Expert verified
Yes, at a .01 level of significance, the data suggests that the average time it takes for individuals with a B.S. degree in accounting to change jobs is significantly more than 2 years.

Step by step solution

01

State the Hypotheses

Null Hypothesis \(H_0\): The average time to change accounting jobs is equal or less than 2 years, i.e., \(μ ≤ 24\). \n Alternative Hypothesis \(H_1\): The average time to change accounting jobs exceeds 2 years, i.e., \(μ > 24\). \n \(H_0\) and \(H_1\) are complementary to each other.
02

Assume Standard Distribution

Since the sample size is greater than 30 (\(n = 44\)), we'll use the standard normal (z) distribution for this hypothesis test. Calculate the test statistic using the formula: \[ z = \frac{\( \bar{x} - μ_0 \)}{\(s/\sqrt{n}\)} \] where \( \bar{x} = 35.02 \), \( μ_0 = 24 \), \( s = 18.94 \), and \( n = 44 \).
03

Calculate Test Statistic

Substitute the given values into the z-formula: \[ z = \frac{35.02 - 24}{18.94/ \sqrt{44}} = 4.60 \] The test statistic \(z = 4.60\) is greater than the critical z-value for a .01 level of significance (2.33).
04

Conclusion

Reject the null hypothesis \(H_0\) if the calculated z-value is greater than the critical z-value. In this case, as the calculated value \(4.60\) exceeds the critical z-value \(2.33\), therefore we reject the null hypothesis. Hence, it can be concluded that the true average time to change jobs for individuals with a B.S. degree in accounting significantly exceeds 2 years at a .01 level of significance.

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Most popular questions from this chapter

In a study of computer use, 1000 randomly selected Canadian Internet users were asked how much time they spend using the Internet in a typical week (Ipsos Reid, August 9,2005 ). The mean of the 1000 resulting observations was \(12.7\) hours. a. The sample standard deviation was not reported, but suppose that it was 5 hours. Carry out a hypothesis test with a significance level of \(.05\) to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than \(12.5\) hours. b. Now suppose that the sample standard deviation was 2 hours. Carry out a hypothesis test with a significance level of . 05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than \(12.5\) hours.

The article referenced in Exercise \(10.34\) also reported that 470 of 1000 randomly selected adult Americans thought that the quality of movies being produced was getting worse. a. Is there convincing evidence that fewer than half of adult Americans believe that movie quality is getting worse? Use a significance level of \(.05\). b. Suppose that the sample size had been 100 instead of 1000 , and that 47 thought that the movie quality was getting worse (so that the sample proportion is still . 47 ). Based on this sample of 100 , is there convincing evidence that fewer than half of adult Americans believe that movie quality is getting worse? Use a significance level of \(.05\). c. Write a few sentences explaining why different conclusions were reached in the hypothesis tests of Parts (a) and (b).

The power of a test is influenced by the sample size and the choice of significance level. a. Explain how increasing the sample size affects the power (when significance level is held fixed). b. Explain how increasing the significance level affects the power (when sample size is held fixed).

To determine whether the pipe welds in a nuclear power plant meet specifications, a random sample of welds is selected and tests are conducted on each weld in the sample. Weld strength is measured as the force required to break the weld. Suppose that the specifications state that the mean strength of welds should exceed 100 \(\mathrm{lb} / \mathrm{in} .^{2}\). The inspection team decides to test \(H_{0}: \mu=100\) versus \(H_{a}: \mu>100 .\) Explain why this alternative hypothesis was chosen rather than \(\mu<100\).

Give as much information as you can about the \(P\) -value of a \(t\) test in each of the following situations: a. Two-tailed test, \(\mathrm{df}=9, t=0.73\) b. Upper-tailed test, \(\mathrm{df}=10, t=-0.5\) c. Lower-tailed test, \(n=20, t=-2.1\) d. Lower-tailed test, \(n=20, t=-5.1\) e. Two-tailed test, \(n=40, t=1.7\)
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