Would you favor spending more federal tax money on the arts? Ofa random sample of n1 = 204 women,r1 = 56 responded yes. Another random sample ofn2 = 193 men showed that r2= 47 responded yes. Does this information indicate a difference(either way) between the population proportion of women and thepopulation proportion of men who favor spending more federal taxdollars on the arts? Use α = 0.10. Solve the problem usingboth the traditional method and the P-value method. (Testthe difference p1 − p2.Round the test statistic and critical value to two decimal places.Round the P-value to four decimal places.)
| teststatistic     | | |
| critical value | ± | |
| P-value | | |
Conclusion
Fail to reject the null hypothesis, there is sufficient evidencethat the proportion of women favoring more tax dollars for the artsis different from the proportion of men.Reject the null hypothesis,there is sufficient evidence that the proportion of women favoringmore tax dollars for the arts is different from the proportion ofmen.    Reject the null hypothesis, there isinsufficient evidence that the proportion of women favoring moretax dollars for the arts is different from the proportion ofmen.Fail to reject the null hypothesis, there is insufficientevidence that the proportion of women favoring more tax dollars forthe arts is different from the proportion of men.
Compare your conclusion with the conclusion obtained by using theP-value method. Are they the same?
We reject the null hypothesis using the P-value method,but fail to reject using the traditional method.These two methodsdiffer slightly.    The conclusions obtained byusing both methods are the same.We reject the null hypothesis usingthe traditional method, but fail to reject using theP-value method.
