Question

HOMEWORK 3 (part3):

3) You now wish to concern yourself with a comparison of the proportions of the supporters of the candidate based upon gender concerning their assertions of party loyalty. Specifically, you wish to know whether the proportion of men that supports the candidate that describes itself as party loyalists is less than the proportion of women that feels the same. The sample data concerning whether the supporter describes himself or herself as a party loyalist is also shown in appendix two below. At both the 2% and 5% levels of significance, is the proportion of male supporters that describes itself as party loyalists less than the proportion of female supporters of the candidate that describes itself as party loyalists? If the procedure you have chosen for this problem allows it (using PHStat) to construct confidence intervals for the difference in the proportions of male and female supporters that describes itself as party loyalists, construct 98% and 95% confidence intervals for the difference in the proportions, and explain their meanings in the context of the problem.

Appendix Two:

Male Supporter Loyalty? (Y = party loyalist, N = not a party loyalist)

Y   N         Y         Y         Y         N         Y         N         Y         N         Y         N

Y   Y         Y         Y         Y         Y         Y         Y         N         Y         Y         Y

Y   Y         N         Y         Y         Y

Female Supporter Loyalty? (Y = party loyalist, N = not a party loyalist)

Y   Y         Y         Y         N         Y         N         Y         Y         Y         N         Y

Y   Y         N         Y         Y         Y         Y         Y         Y         Y         Y         Y

Y   Y         Y         Y         Y         Y

Answer 1

For male supporter:

Sample size, n₁ = 30

Number of male loyalist = 23

Proportion of male loyalist, P₁ = 23/30 = 0.767

For female supporter:

Sample size, n₂ = 30

Number of female loyalist = 26

Proportion of female loyalist, P₂ = 26/30 = 0.867

Now, total proportion of loyalist, p = (23+26)/(30+30) = 0.817

Standard error, SE = sqrt{ p * ( 1 - p ) * [ (1/n₁) + (1/n₂) ] } = sqrt[0.817 * 0.183 * (1/30 + 1/30)]= 0.1

z = (P2 - P1) / SE = (0.867- 0.767) / 0.1 = 1

For 95% confidence interval z= 1.96

For 98% confidence interval z= 2.33

Let null hypothesis be: proportion of male supporters that describes itself as party loyalists are significantly less than the proportion of female supporters of the candidate that describes itself as party loyalists

The z values for 95% and 98% confidence interval are greater than the z value that we calculated (1), hence we reject null hypothesis.

This means that at 95% and 98% confidence intervals, proportion of male supporters that describes itself as party loyalists are not significantly less than the proportion of female supporters of the candidate that describes itself as party loyalists.