One of the consequences of the economic meltdown has been a free fall of the stock market’s average price/earnings ratio, or P/E ratio (The Wall Street Journal, August 30, 2010). Generally, a high P/E ratio suggests that investors are expecting higher earnings growth in the future compared to companies with a lower P/E ratio. An analyst wants to determine if the P/E ratio of firms in the footwear industry is different from the overall average of 14.9. The table below shows the P/E ratios for a sample of seven firms in the footwear industry:
Firm P/E Ratio
Brown Shoe Co., Inc..... 20.54
Collective Brands, Inc. ..... 9.33
Crocs, Inc. .......... 22.63
DSW, Inc. .......... 14.42
Nike, Inc. .......... 18.68
Skechers USA, Inc. ..... 9.35
Timberland Co. ..... 14.93
a. State the null and the alternative hypotheses in order to test whether the P/E ratio of firms in the footwear industry differs from the overall average of 14.9.
b. What assumption regarding the population is necessary?
c. Use Excel to calculate the value of the test statistic and the exact p-value.
d. At α = 0.10, does the P/E ratio of firms in the footwear industry differ from the overall average of 14.9? Explain.