The price to earnings ratio (P/E) is an important tool in financial work. A random sample of 14 large U.S. banks (JP Morgan Chase, 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= 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 H= 18. 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 a- 4.7. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? 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-talled test? O Ho: H = 18; H: H+ 18; two-tailed O Ho: H = 18; H: H < 18; left-tailed O Ho: H = 18; H1: µ > 18; right-tailed O Ho: H * 18; H: H- 18; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution with unknown a. O The Student's t, sincen is large with unknown a. O The standard normal, since we assume that x has a normal distribution with known 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 earnings ratio (P/E) is an important tool in financial work. A random sample of 14 large U.S. banks (JP Morgan Chase, 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= 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 H= 18. 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 a- 4.7. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? 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-talled test? O Ho: H = 18; H: H+ 18; two-tailed O Ho: H = 18; H: H < 18; left-tailed O Ho: H = 18; H1: µ > 18; right-tailed O Ho: H * 18; H: H- 18; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution with unknown a. O The Student's t, sincen is large with unknown a. O The standard normal, since we assume that x has a normal distribution with known 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.)
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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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 (JP Morgan Chase, 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 = 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
H = 18. 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 = 4.7. Do these data indicate that the P/E ratio of all
U.S. bank stocks is less than 18? 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 = 18; H1: H # 18; two-tailed
O Ho: H = 18; H1: H < 18; left-tailed
O Ho: H = 18; H1: µ > 18; right-tailed
%3D
O Ho: H # 18; H1: H = 18; two-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
O The standard normal, since we assume that x has a normal distribution with unknown o.
O The Student's t, since n is large with unknown o.
O The standard normal, since we assume that x has a normal distribution with known 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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