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 = 19. 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 = 5.5. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 19? Use α = 0.01. (a) What is the level of significance?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.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
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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.†

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 = 19. 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 = 5.5. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 19? Use α = 0.01.

(a) What is the level of significance?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.)

 
Expert Solution
Step 1

The null and the alternative hypotheses are,

H0: µ≥19

HA: µ<19

(a)

The level of significance α is 0.01.

Test statistic:

Statistics homework question answer, step 1, image 1

Thus, the test statistic is -1.30.

 

Step 2

(c)

The P-value is calculated using Excel software:

Statistics homework question answer, step 2, image 1

Thus, the P-value is 0.0968.

 

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