The price to eanings ratio (P/E) is an important tool in financial work. A random sample of 14 large U.S. banks (3. P. Morgan, Bank of America, and others) gave the following P/E ratios. 24 16 22 14 12 13 17 22 15 19 23 13 11 18 The sample mean is xx 17.1. Generally speaking, a low P/E ratio indicates a "value" or bargain stock. Suppose a recent copy of a magazine indicated that the P/E ratio of a certain stock index is u= 19. Let x be a random variable representing the P/E ratio of all large U.S. bank stocks. We assume that x has a normal distribution and o = 3.9. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 19? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: H= 19; H: H > 19; right-tailed O Ho: H= 19; H: H = 19; two-tailed O Hgi H= 19; H: H2 19; two-tailed O Họ: H = 19; H: H< 19; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since n is large with unknown a. O The standard normal, since we assume that x has a normal distribution with known a. O The standard normal, since we assume that x has a normal distribution with unknown o. O The Student's t, since we assume that x has a normal distribution with known a. Compute the z 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.)
The price to eanings ratio (P/E) is an important tool in financial work. A random sample of 14 large U.S. banks (3. P. Morgan, Bank of America, and others) gave the following P/E ratios. 24 16 22 14 12 13 17 22 15 19 23 13 11 18 The sample mean is xx 17.1. Generally speaking, a low P/E ratio indicates a "value" or bargain stock. Suppose a recent copy of a magazine indicated that the P/E ratio of a certain stock index is u= 19. Let x be a random variable representing the P/E ratio of all large U.S. bank stocks. We assume that x has a normal distribution and o = 3.9. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 19? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: H= 19; H: H > 19; right-tailed O Ho: H= 19; H: H = 19; two-tailed O Hgi H= 19; H: H2 19; two-tailed O Họ: H = 19; H: H< 19; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since n is large with unknown a. O The standard normal, since we assume that x has a normal distribution with known a. O The standard normal, since we assume that x has a normal distribution with unknown o. O The Student's t, since we assume that x has a normal distribution with known a. Compute the z 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.)
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The price to earnings ratio (P/E) is an important tool in financial work. A random sample of 14 large U.S. banks (J. P. Morgan, Bank of America, and others) gave the following P/E ratios.†
24 16 22 14 12 13 17 22 15 19 23 13 11 18
Transcribed Image Text:The price to earnings ratio (P/E) is an important tool in financial work. A random sample of 14 large U.S. banks (J. P. Morgan, Bank of America, and others) gave the following P/E ratios.t
24 16 22 14 12 13 17 22 15 19 23 13
11 18
The sample mean is x x 17.1. Generally speaking, a low P/E ratio indicates a "value" or bargain stock. Suppose a recent copy of a magazine indicated that the P/E ratio of a certain stock index is u = 19. Let x be a random variable representing the P/E ratio of all large
U.S. bank stocks. We assume that x has a normal distribution and o = 3.9. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 19? Use a = 0.01.
(a) What is the level of significance?
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
O Ho: u = 19; H: µ > 19; right-tailed
O Ho: µ # 19; H,: µ = 19; two-tailed
O Ho: H = 19; H;: µ # 19; two-tailed
O Ho: H = 19; H,: µ < 19; left-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
O The Student's t, sincen is large with unknown o.
O The standard normal, since we assume that x has a normal distribution with known o.
O The standard normal, since we assume that x has a normal distribution with unknown o.
O The Student's t, since we assume that x has a normal distribution with known o.
Compute the z 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.)
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