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 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 μ = 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 σ = 4.5. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? Use ? = 0.01. (a) What is the level of significance? State the null hypothesis H0 and the alternate hypothesis H1 . H0 : μ ---Select--- ≥ > ≤ ≠ = < H1 : μ ---Select--- ≥ ≠ < > ≤ = What kind of test is this? right-tailed testleft-tailed test two-tailed test (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 σ.The Student's t, since n is small with unknown σ. Compute the sample test statistic based on your choice of the distribution. (Round your answer to two decimal places.) (c) Find the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. (d) Based on your answers in the previous parts, state your decision. Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?? At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) State your conclusion. There is sufficient evidence at the 0.01 level to conclude that the P/E ratio of all large U.S. bank stocks is less than 18There is insufficient evidence at the 0.01 level to conclude that the P/E ratio of all large U.S. bank stocks is less than 18

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 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 μ = 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 σ = 4.5. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? Use ? = 0.01. (a) What is the level of significance? State the null hypothesis H0 and the alternate hypothesis H1 . H0 : μ ---Select--- ≥ > ≤ ≠ = < H1 : μ ---Select--- ≥ ≠ < > ≤ = What kind of test is this? right-tailed testleft-tailed test two-tailed test (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 σ.The Student's t, since n is small with unknown σ. Compute the sample test statistic based on your choice of the distribution. (Round your answer to two decimal places.) (c) Find the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. (d) Based on your answers in the previous parts, state your decision. Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?? At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) State your conclusion. There is sufficient evidence at the 0.01 level to conclude that the P/E ratio of all large U.S. bank stocks is less than 18There is insufficient evidence at the 0.01 level to conclude that the P/E ratio of all large U.S. bank stocks is less than 18

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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.†

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 μ = 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 σ = 4.5. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? Use ? = 0.01.

(a) What is the level of significance?

State the null hypothesis

H₀

and the alternate hypothesis

H₁

H₀

: μ ---Select--- ≥ > ≤ ≠ = <

H₁

: μ ---Select--- ≥ ≠ < > ≤ =

What kind of test is this?

right-tailed testleft-tailed test two-tailed test

(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 σ.The Student's t, since n is small with unknown σ.

Compute the sample test statistic based on your choice of the distribution. (Round your answer to two decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in the previous parts, state your decision. Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) State your conclusion.

There is sufficient evidence at the 0.01 level to conclude that the P/E ratio of all large U.S. bank stocks is less than 18There is insufficient evidence at the 0.01 level to conclude that the P/E ratio of all large U.S. bank stocks is less than 18

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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