Question

The yield of Australia bank stocks has a normal distribution with s.d. 0.024. A random sample of 10 Australian bank stocks gave the mean yield 0.0538. For the entire Australia stock market, the mean dividend yield is 0.047. Does this indicate that the dividend yield of all Australia bank stock is higher than 0.047? Let alpha = .01, do a hypothesis test.

a. test statement: null/alternative

b. calculate test statistic.

c. Find the critical value and draw a graph to find the reject region. Then make your decision.

d. Find the p value and draw a graph to mark the p value. Then make your decision.

e. Give your conclusion in a way that non-staticians can understand.

Answer 1

a) H₀: = 0.047

    H₁: > 0.047

b) The test statistic z = ()/()

                                  = (0.0538 - 0.047)/(0.024/)

                                  = 0.90

c) At alpha = 0.01, the critical value is z_0.99 = 2.33

Reject H₀, if z > 2.33

Since the test statistic value is not greater than the critical value(0.90 < 2.33), so we should not reject the null hypothesis.

d) P-value = P(Z > 0.90)

                 = 1 - P(Z < 0.90)

                 = 1 - 0.8159

                 = 0.1841

e) At alpha = 0.01, there is not sufficient evidence to support the claim that the dividend yield of all Australia bank stock is higher than 0.047.