Question

25.

Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with σ = 2.6%. A random sample of 17 Australian bank stocks has a sample mean of x = 8.76%. For the entire Australian stock market, the mean dividend yield is μ = 6.5%. Do these data indicate that the dividend yield of all Australian bank stocks is higher than 6.5%? Use α = 0.01. Are the data statistically significant at the given level of significance? Based on your answers, will you reject or fail to reject the null hypothesis?

Select one:

a. The P-value is greater than than the level of significance and so the data are not statistically significant. Thus, we fail to reject the null hypothesis.

b. The P-value is less than than the level of significance and so the data are statistically significant. Thus, we reject the null hypothesis.

c. The P-value is greater than than the level of significance and so the data are statistically significant. Thus, we reject the null hypothesis.

d. The P-value is less than than the level of significance and so the data are not statistically significant. Thus, we reject the null hypothesis.

e. The P-value is less than than the level of significance and so the data are statistically significant. Thus, we fail to reject the null hypothesis.

(E is not the answer)

Answer 1

25)

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 0.065

H_a : > 0.065

= 0.0876

= 0.065

= 0.026

n = 17

Test statistic = z

= ( - ) / / n

= (0.0876 - 0.065) / 0.026 / 17

= 3.58

Test statistic = 3.58

This is the right tailed test .

P(z > 3.58) = 1 - P(z < 3.58) = 1 - 0.9998 = 0.0002

P-value = 0.0002

= 0.01

P-value <

Reject the null hypothesis .

b. The P-value is less than than the level of significance and so the data are statistically significant. Thus, we reject the null hypothesis.