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 = 4.1. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? Use α = 0.01. State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: μ = 18; H1: μ ≠ 18; two-tailedH0: μ = 18; H1: μ < 18; left-tailed H0: μ = 18; H1: μ > 18; right-tailedH0: μ ≠ 18; H1: μ = 18; two-tailed (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 unknown σ.The standard normal, since we assume that x has a normal distribution with known σ. The Student's t, since we assume that x has a normal distribution with known σ.The Student's t, since n is large with unknown 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.

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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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 = 4.1. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? Use α = 0.01.

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

H₀: μ = 18; H₁: μ ≠ 18; two-tailedH₀: μ = 18; H₁: μ < 18; left-tailed H₀: μ = 18; H₁: μ > 18; right-tailedH₀: μ ≠ 18; H₁: μ = 18; two-tailed

(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 unknown σ.The standard normal, since we assume that x has a normal distribution with known σ. The Student's t, since we assume that x has a normal distribution with known σ.The Student's t, since n is large with unknown 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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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