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†.
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24
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16
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22
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14
|
12
|
13
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17
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22
|
15
|
19
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23
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13
|
11
|
18
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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 = 4.7. 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?
b) What is the value of the sample test statistic?
c) Find (or estimate) the P-value.