Question

Would you favor spending more federal tax money on the arts? Of a random sample of n₁ = 210 women, r₁ = 56 responded yes. Another random sample of n₂ = 187 men showed that r₂ = 55 responded yes. Does this information indicate a difference (either way) between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts? Use α = 0.05. Solve the problem using both the critical region method and the P-value method. (Test the difference p₁ − p₂. Round the test statistic and critical value to two decimal places. Round the P-value to four decimal places.)

1) z-statistic = ?

2) critical value = ?

3) p-value = ?

4) Conclusion

a) Reject the null hypothesis, there is sufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men.

b) Fail to reject the null hypothesis, there is insufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men.  

c) Reject the null hypothesis, there is insufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men.

d) Fail to reject the null hypothesis, there is sufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men.

5) Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?

a) We reject the null hypothesis using the P-value method, but fail to reject using the critical region method.

b) These two methods differ slightly.    

c) The conclusions obtained by using both methods are the same.

d) We reject the null hypothesis using the critical region method, but fail to reject using the P-value method.

Answer 1

Here

The hypotheses are

a) The test statistic

b) The critical value is

c) The p-value is

d) Since , we fail to reject the null hypothesis. The proportions are not different.

Conclusion:

b) Fail to reject the null hypothesis, there is insufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men.

e) By critical value method, . Hence, we fail to reject the null hypothesis.

c) The conclusions obtained by using both methods are the same.