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 isx17.1.

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=18.Letxbe a random variable representing theP/E ratioof all largeU.S. bankstocks. We assume thatxhas a normal distribution and=5.4.Do these data indicate that theP/E ratioof allU.S. bankstocks is less than18? 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?

H₀:= 18;H₁:< 18; left-tailed

H₀:18;H₁:= 18; two-tailed

H₀:= 18;H₁:18; two-tailed

H₀:= 18;H₁:> 18; right-tailed

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

The Student'st, since we assume thatxhas a normal distribution with known.

The Student'st, sincenis large with unknown.

The standard normal, since we assume thatxhas a normal distribution with unknown.

The standard normal, since we assume thatxhas a normal distribution with known.

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?

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 in the context of the application.

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 18

There 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 18