Letxbe a random variable representing dividend yield of bank stocks. We may assume thatxhas a normal distribution with=3.0%.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=4.1%.Do these data indicate that the dividend yield of all bank stocks is higher than4.1%? 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:= 4.1%;H₁:4.1%; two-tailed

H₀:= 4.1%;H₁:<4.1%; left-tailed

H₀:= 4.1%;H₁:>4.1%; right-tailed

H₀:>4.1%;H₁:= 4.1%; 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 standard normal, 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.)