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# Calculate the sample mean and standard deviation for the variables P/E ratio, Div. yd., NTA/share

(a) Using the sample data attached, calculate the sample mean and standard deviation for the variables: - a. P/E Ratio (3 marks) b. Div. yd. (%) (3 marks) c. NTA/Share (3 marks) (b) Is there any evidence of skewness in the data sets? Which data set displays greatest skewness? (3 marks) (c) Using the sample data on P/E Ratio, calculate the sample proportion of companies whose P/E Ratio exceeds 20 and its corresponding standard deviation. (3 marks) (d) Set up and interpret the following confidence intervals â€“ i. A 95% confidence interval for the true population mean P/E ratio (3 marks) ii. A 99% confidence interval for the true population mean Div yld (%) (3 marks) iii. A 90% confidence interval to estimate the true population proportion of all companies whose P/E Ratio is better than 20. (3 marks) (e) A follow-up study will provide a point estimate of the population proportion of companies with a P/E ratio that exceeds 23. The study must provide 90% confidence that the point estimate is within 0.10 of the population proportion. If no previous proportion estimate is available (not even that calculated in (c) above), how large a sample would you recommend for this study? (4 marks) (f) Stock market analysts claim that on average the P/E ratio of all companies in the ASX 50 is more than 18. Do the data provide significant support for this claim? Use a 5% significance level and the critical value approach (classical approach) to test this claim. (6 marks) (g) JASSA, the latest Finance journal, has claimed that less than 30% of all companies in the ASX 50 have a dividend yield (%) that is 10 or more. How much evidence do the data provide to support this claim? Use a 0.05 level of significance and the p-value approach to test this claim. (6 marks) (h) The ASX claims that the average Net Tangible Assets for companies in the ASX50 is 3.5. Test this claim at alpha = 0.01. (6 marks) (i) Imagine that your sample data set only included the first fifteen companies with the largest market capitalisation listed in your original data set. For this new data set, you are now told that the P/E ratio of companies has followed the normal distribution in the past. With this reduced data set, test the claim that on average the P/E ratio of all companies is more than 18 at the1% significance level. Compare this result to your answer if Part A (f). Can you suggest any reasons for the variation, if one exists. (6 marks)