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.†
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. Letx be a random variable representing the P/E ratio of all large U.S. bank stocks. We assume thatx has a normal distribution and σ = 4.8. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 19? 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?
H
0: μ = 19;H
1: μ > 19; right-tailedH
0: μ = 19;H
1: μ < 19;="">H
0: μ ≠ 19;H
1: μ = 19; two-tailedH
0: μ = 19;H
1: μ ≠ 19; two-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The Student'st, sincen is large with unknown σ.The standard normal, since we assume thatx has a normal distribution with unknown σ. The Student'st, since we assume thatx has a normal distribution with known σ.The standard normal, since we assume thatx has a normal distribution with known σ.
Compute the
z value of the sample test statistic. (Round your answer to two decimal places.)
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(c) Find (or estimate) the
P-value. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to the
P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.