The price-to-earnings (P/E) ratio is an important tool in financial work. A random sample of 14 large U.S. banks (JPMorgan Chase, Bank of America, and others) gave the following P/E ratios:

The sample mean is ‰ˆ 17.1. Generally speaking, a low P/E ratio indicates a €œvalue€ or bargain stock. A recent copy of The Wall Street Journal indicated that the P/E ratio of the entire S&P 500 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 = 4.5. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 19? Use α = 0.05.
Please provide the following information:
(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?
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the value of the sample test statistic.
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a)€“(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(e) Interpret your conclusion in the context of the application.

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