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Chapter 8: Q89E (page 452)
Find a value of the standard normal random variable z, call it , such that
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Buy-side vs. sell-side analysts' earnings forecasts. Refer to the Financial Analysts Journal (Jul. /Aug. 2008) study of financial analysts' forecast earnings, Exercise 2.86 (p. 112). Recall that data were collected from buy-side analysts and forecasts made by sell-side analysts, and the relative absolute forecast error was determined for each. The mean and standard deviation of forecast errors for both types of analysts are given in the table.
a. Construct a confidence interval for the difference between the mean forecast error of buy-side analysts and the mean forecast error of sell-side analysts.
b. Based on the interval, part a, which type of analysis has the greater mean forecast error? Explain.
c. What assumptions about the underlying populations of forecast errors (if any) are necessary for the validity of the inference, part b?
Shared leadership in airplane crews. Refer to the Human Factors (March 2014) study of shared leadership by the cockpit and cabin crews of a commercial airplane, Exercise 8.14 (p. 466). Recall that each crew was rated as working either successfully or unsuccessfully as a team. Then, during a simulated flight, the number of leadership functions exhibited per minute was determined for each individual crew member. One objective was to compare the mean leadership scores for successful and unsuccessful teams. How many crew members would need to be sampled from successful and unsuccessful teams to estimate the difference in means to within .05 with 99% confidence? Assume you will sample twice as many members from successful teams as from unsuccessful teams. Also, assume that the variance of the leadership scores for both groups is approximately .04.
History of corporate acquisitions. Refer to the Academy of Management Journal (August 2008) investigation of the performance and timing of corporate acquisitions, Exercise 2.12 (p. 74). Recall that the investigation discovered that in a random sample of 2,778 firms, 748 announced one or more acquisitions during the year 2000. Does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 30%? Use to make your decision.
Question: The purpose of this exercise is to compare the variability of with the variability of .
a. Suppose the first sample is selected from a population with mean and variance . Within what range should the sample mean vary about of the time in repeated samples of measurements from this distribution? That is, construct an interval extending standard deviations of on each side of .
b. Suppose the second sample is selected independently of the first from a second population with mean and variance . Within what range should the sample mean vary about the time in repeated samples of measurements from this distribution? That is, construct an interval extending standard deviations on each side .
c. Now consider the difference between the two sample means . What are the mean and standard deviation of the sampling distribution ?
d. Within what range should the difference in sample means vary about the time in repeated independent samples of measurements each from the two populations?
e. What, in general, can be said about the variability of the difference between independent sample means relative to the variability of the individual sample means?
Question: Consumers鈥� attitudes toward advertising. The two most common marketing tools used for product advertising are ads on television and ads in a print magazine. Consumers鈥� attitudes toward television and magazine advertising were investigated in the Journal of Advertising (Vol. 42, 2013). In one experiment, each in a sample of 159 college students were asked to rate both the television and the magazine marketing tool on a scale of 1 to 7 points according to whether the tool was a good example of advertising, a typical form of advertising, and a representative form of advertising. Summary statistics for these 鈥渢ypicality鈥� scores are provided in the following table. One objective is to compare the mean ratings of TV and magazine advertisements.
a. The researchers analysed the data using a paired samples t-test. Explain why this is the most valid method of analysis. Give the null and alternative hypotheses for the test.
b. The researchers reported a paired t-value of 6.96 with an associated p-value of .001 and stated that the 鈥渕ean difference between television and magazine advertising was statistically significant.鈥� Explain what this means in the context of the hypothesis test.
c. To assess whether the result is 鈥減ractically significant,鈥� we require a confidence interval for the mean difference. Although this interval was not reported in the article, you can compute it using the information provided in the table. Find a 95% confidence interval for the mean difference and interpret the result. What is your opinion regarding whether the two means are 鈥減ractically significant.鈥�
Source: H. S. Jin and R. J. Lutz, 鈥淭he Typicality and Accessibility of Consumer Attitudes Toward Television Advertising: Implications for the Measurement of Attitudes Toward Advertising in General,鈥� Journal of Advertising, Vol. 42, No. 4, 2013 (from Table 1)
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