In: Math
One of the consequences of the economic meltdown in Great Recession has been a free fall of the stock market's average price/earning ratio, or P/E ratio. Generally, a high P/E ratio suggest that investors are expecting higher earnings growth in the future compared to companies with a lower P/E ratio. A Wall Street analyst wants to determine if the P/E ratio of rms in the footwear industry is dierent from the overall average of 20. The table below shows that P/E ratio for a sample of six rms in the footwear industry: Firm P/E ratio Collective Brands, Inc. 9.33 Cros,Inc. 22.63 DSW, Inc. 14.42 Nike, Inc. 18.68 Sketchers USA, Inc 9.35 Timberland Co. 14.93 a. (3 points) Let µ be the overall average P/E ratio. State the null and the alternative hypothesis in order to test whether the P/E ratio of rms in the footwear industry diers from the overall average of 20. b. (3 points) What is the average P/E ratio among the six footwear rms, i.e., x¯ =? c. (3 points) What is the standard deviation of the P/E ratio among the six footwear rms, i.e., s =? (Please around your answer to 4 decimal places. d. (3 points) Construct a 90% condence interval of the overall average P/E ratio, i.e., 90% condence interval of µ. (Please around your answer to 4 decimal places.) e. (2 point) Calculate the value of test statistic. (Please around your answer to 3 decimal places.) f. (4 points) Approximate the p-value in this test? g. (3 points) Does the P/E ratio of rms in the footwear industry dier from the overall average of 20? Please explain.