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 isx17.1. Generally speaking, a low P/E ratio indicates a "value" or bargain stock. Suppose a recent copy of a magazine indicated that theP/E ratioof a certain stock index is=19.Letxbe a random variable representing theP/E ratioof all largeU.S. bankstocks. We assume thatxhas a normal distribution and=5.1.Do these data indicate that theP/E ratioof allU.S. bankstocks is less than19? Use=0.01.

(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 thezvalue of the sample test statistic. (Round your answer to two decimal places.)

(c) Find (or estimate) theP-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to theP-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?

(e) State your conclusion in the context of the application.