Question

Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.9%. A random sample of 10 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 x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.9%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.9%? Use α = 0.01.

(a) What is the level of significance?

0.01

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

H₀: μ = 4.9%; H₁:  μ > 4.9%; right-tailed

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

The standard normal, since we assume that x has a normal distribution with known σ.

Compute the z value of the sample test statistic. (Round your answer to two decimal places.)

(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Answer 1

The statistical software output for this problem is:

Hence,

b) Test statistic = 0.52

c) P - value = 0.3003