Letxbe a random variable representing dividend yield of bank stocks. We may assume thatxhas a normal distribution with=3.1%.A random sample of10 bankstocks gave the following yields (in percents).

5.74.86.04.94.03.46.57.15.36.1

The sample mean is= 5.38%. Suppose that for the entire stock market, the mean dividend yield is=4.9%.Do these data indicate that the dividend yield of all bank stocks is higher than4.9%? Use=0.01.

(a)

What is the level of significance? (Enter a number.)

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

H₀:= 4.9%;H₁:<4.9%; left-tailed

H₀:>4.9%;H₁:= 4.9%; right-tailed

H₀:= 4.9%;H₁:>4.9%; right-tailed

H₀:= 4.9%;H₁:4.9%; two-tailed

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

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

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.

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

(c)

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

Sketch the sampling distribution and show the area corresponding to theP-value. (Select the correct graph.)

(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 average yield for bank stocks is higher than that of the entire stock market.

There is insufficient evidence at the 0.01 level to conclude that the average yield for bank stocks is higher than that of the entire stock market.