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.)
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
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
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
The null and the alternative hypotheses are,
H0: µ≥19
HA: µ<19
(a)
The level of significance α is 0.01.
Test statistic:
Thus, the test statistic is -1.30.
(c)
The P-value is calculated using Excel software:
Thus, the P-value is 0.0968.
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