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.2416221412131722151923131118The sample mean isx17.071.

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=3.7.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 hypothesisH₀

and the alternate hypothesisH₁

.

H₀

:

H₁

:

What kind of test is this?

right-tailed testtwo-tailed testleft-tailed test

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student'st, sincenis small with unknown.The standard normal, since we assume thatxhas a normal distribution with known.

Compute the sample test statistic based on your choice of the distribution. (Round your answer to two decimal places.)

(c) Find 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 the previous parts, state your decision. Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?

At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) State your conclusion.

There is sufficient evidence at the 0.01 level to conclude that the P/E ratio of all large U.S. bank stocks is less than 19There is insufficient evidence at the 0.01 level to conclude that the P/E ratio of all large U.S. bank stocks is less than 19