11. [-/9 Points] DETAILS BBBASICSTAT8 7.R.015.S. MY NOTES Given that x is a normal variable with mean y = 48 and standard deviation o = 6.8, find the following probabilities. (Round your answers to four decimal places.) LO USE SALT (a) P(x 5 60) (b) P(x 2 50) (c) P(50 4.55 g; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. " The standard normal, since we assume that x has a normal distribution with known 0'. ' The Student's t, since n is large with unknown or. ' The Student's t, since we assume that X has a normal distribution with known a. ' The standard normal, since we assume that x has a normal distribution with unknown 0'. Compute the 2 value of the sample test statistic. (Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. A ,3 2 1 0 1 2 3 \"3 -2 -1 0 1 2 3 ,3 2 1 D 1 2 3 \"3 2 1 0 1 2 3 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically signicant at level a? '\\ At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically signicant. At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically signicant. At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically signicant. At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically signicant. (e) State your conclusion in the context of the application. There is sufficient evidence at the 0.01 level to conclude that humming birds in the Grand Canyon weigh less than 4.55 grams. There is insufficient evidence at the 0.01 level to conclude that humming birds in the Grand Canyon weigh less than 4.55 grams.18. [-/24 Points] DETAILS BBBASICSTAT8 9.2.015.S. MY NOTES 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 u = 19.4. A random sample of 36 "socially conscious" stocks gave a P/E ratio sample mean of x = 17.8, with sample standard deviation s = 5.8. 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 a = 0.05. LO USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Ho: M = 19.4; H: M # 19.4 O Ho: M = 19.4; H1: M 19.4; H1: M = 19.4 O Ho: M = 19.4; H1: M > 19.4 O Ho: M # 19.4; H1: M = 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 o is known. The standard normal, since the sample size is large and o is known. The Student's t, since the sample size is large and o is unknown. The standard normal, since the sample size is large and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.)(c) Estimate the P-value. O P-value > 0.250 0.100