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 = 5.3. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 18? Use α = 0.05.
(a) What is the level of significance?
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-tailed
H0: μ = 18; H1: μ > 18; right-tailed
H0: μ = 18; H1: μ ≠ 18; two-tailed
H0: μ = 18; H1: μ < 18; left-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
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.
The standard normal, since we assume that x has a normal distribution with known σ.
The standard normal, since we assume that x has a normal distribution 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.)
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