if it is possible to show work for question 5 and 11. In total there is 5 questions.

Question 5 Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with = 2.3%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is = 4.5%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.5%? Use = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or twotailed test? Which one from below. H0: = 4.5%; H1: 4.5%; two-tailed H0: = 4.5%; H1: > 4.5%; right-tailed H0: > 4.5%; H1: = 4.5%; right-tailed H0: = 4.5%; H1: 18; right-tailed H0: = 18; H1: 1.75 yr H0: 1.75 yr; H1: = 1.75 yr (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and is unknown. The standard normal, since the sample size is large and is known. The Student's t, since the sample size is large and is known. The Student's t, since the sample size is large and is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find the P-value. (Round your answer to four decimal places.) 10. Socially conscious investors screen out stocks of alcohol and tobacco makers, firms with poor environmental records, and companies with poor labor practices. Some examples of "good," socially conscious companies are Johnson and Johnson, Dell Computers, Bank of America, and Home Depot. The question is, are such stocks overpriced? One measure of value is the P/E, or price-to-earnings ratio. High P/E ratios may indicate a stock is overpriced. For the S&P Stock Index of all major stocks, the mean P/E ratio is = 19.4. A random sample of 36 "socially conscious" stocks gave a P/E ratio sample mean of x = 18.5, with sample standard deviation s = 4.8. Does this indicate that the mean P/E ratio of all socially conscious stocks is different (either way) from the mean P/E ratio of the S&P Stock Index? Use = 0.10. (a) What is the level of significance? State the null and alternate hypotheses. H0: H0: H0: H0: H0: = 19.4; H1: 19.4 > 19.4; H1: = 19.4 = 19.4; H1: 19.4 19.4; H1: = 19.4 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since the sample size is large and is unknown. The standard normal, since the sample size is large and is unknown. The Student's t, since the sample size is large and is known. The standard normal, since the sample size is large and is known. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find the P-value. (Round your answer to four decimal places.) 11. The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate d.f. as the row header. For a right-tailed test, the column header is the value of found in the one-tail area row. For a left-tailed test, the column header is the value of found in the one-tail area row, but you must change the sign of the critical value t to t. For a two-tailed test, the column header is the value of from the two-tail area row. The critical values are the t values shown. Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is = 19 inches. However, a survey reported that of a random sample of 51 fish caught, the mean length was x = 18.4 inches, with estimated standard deviation s = 2.6 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than = 19 inches? Use = 0.05. Solve the problem using the critical region method of testing (i.e., traditional method). (Round the your answers to three decimal places.) test statistic = critical value = State your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that the average fish length is less than 19 inches. Reject the null hypothesis, there is insufficient evidence that the average fish length is less than 19 inches. Fail to reject the null hypothesis, there is sufficient evidence that the average fish length is less than 19 inches. Fail to reject the null hypothesis, there is insufficient evidence that the average fish length is less than 19 inches. Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same? The conclusions obtained by using both methods are the same. We reject the null hypothesis using the traditional method, but fail to reject using the P-value method. We reject the null hypothesis using the P-value method, but fail to reject using the traditional method