In an article in the Journal of Retailing, Kumar, Kerwin, and Pereira study factors affecting merger and acquisition activity in retailing. As part of the study, the authors compare the characteristics of “target firms” (firms targeted for acquisition) and “bidder firms” (firms attempting to make acquisitions). Among the variables studied in the comparison were earnings per share, debt-to-equity ratio, growth rate of sales, market share, and extent of diversification.
a. Let μ be the mean growth rate of sales for all target firms (firms that have been targeted for acquisition in the last five years and that have not bid on other firms), and assume growth rates are approximately normally distributed. Furthermore, suppose a random sample of 25 target firms yields a sample mean sales growth rate of 0.16 with a standard deviation of 0.12. Use critical values and this sample information to test H0: μ ≤ .10 versus Ha: μ > .10 by setting a equal to .10, .05, .01, and .001. How much evidence is there that the mean growth rate of sales for target firms exceeds .10 (that is, exceeds 10 percent)?
b. Now let m be the mean growth rate of sales for all firms that are bidders (firms that have bid to acquire at least one other firm in the last five years), and again assume growth rates are approximately normally distributed. Furthermore, suppose a random sample of 25 bidders yields a sample mean sales growth rate of 0.12 with a standard deviation of 0.09. Use critical values and this sample information to test H0: μ ≤ .10 versus Ha: μ > .10 by setting α equal to .10, .05, .01, and .001. How much evidence is there that the mean growth rate of sales for bidders exceeds .10 (that is, exceeds 10 percent)?