Answered: The price to earnings ratio (P/E) is an…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 4GP

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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.†

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 ? = 20. 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 ? = 5.1. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 20? Use ? = 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?

H₀: ? ≠ 20; H₁: ? = 20; two-tailed

H₀: ? = 20; H₁: ? < 20; left-tailed

H₀: ? = 20; H₁: ? ≠ 20; two-tailed

H₀: ? = 20; H₁: ? > 20; right-tailed

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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