Letxbe a random variable representing dividend yield of bank stocks. We may assume thatxhas a normal distribution with=2.5%.A random sample of10 bankstocks gave the following yields (in percents).

• 5.7
• 4.8
• 6.0
• 4.9
• 4.0
• 3.4
• 6.5
• 7.1
• 5.3
• 6.1

The sample mean is= 5.38%. Suppose that for the entire stock market, the mean dividend yield is=4.2%.Do these data indicate that the dividend yield of all bank stocks is higher than4.2%? 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:= 4.2%;H₁:>4.2%; right-tailedH₀:= 4.2%;H₁:<4.2%; left-tailed H₀:>4.2%;H₁:= 4.2%; right-tailedH₀:= 4.2%;H₁:4.2%; 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.)