Question

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.†

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 = 4.2. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? Use α = 0.05.

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.)

(e) State your conclusion in the context of the application.

A. There is sufficient evidence at the 0.05 level to conclude that the P/E ratio of all large U.S. bank stocks is less than 18

B. There is insufficient evidence at the 0.05 level to conclude that the P/E ratio of all large U.S. bank stocks is less than 18    

Answer 1

H0: mu = 18
Ha: mu < 18

xbar = 17.1, sigma = 4.2
n = 14

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (17.1 - 18)/(4.2/sqrt(14))
z = -0.8

c)
this is left tailed test, p-value = P(z < -0.8)
p-value = 0.2119

e)
There is insufficient evidence at the 0.05 level to conclude that the P/E ratio of all large U.S. bank stocks is less than 18