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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 = 4.4. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? Use α = 0.05.

(a) State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

a) H₀: μ = 18; H₁: μ > 18; right-tailed

b) H₀: μ = 18; H₁: μ < 18; left-tailed

c) H₀: μ ≠ 18; H₁: μ = 18; two-tailed

d) H₀: μ = 18; H₁: μ ≠ 18; two-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

a) The Student's t, since we assume that x has a normal distribution with known σ.

b) The Student's t, since n is large with unknown σ.

c) The standard normal, since we assume that x has a normal distribution with unknown σ.

d) The standard normal, since we assume that x has a normal distribution with known σ.

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.)

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

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

a) At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

b) At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

c) At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

d) At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

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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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