The research group asked the following question of individuals who earned in exc
ID: 3222659 • Letter: T
Question
The research group asked the following question of individuals who earned in excess of $100, 000 per year and those who earned less than $100, 000 per year. "Do you believe that it is morally for unfed women to have children?" Of the 1.205 individuals who earned in excess of $100, 000 per year, 715 said yes, of the 1, 310 individuals who earned less than $100, 000 per year, said yes. Construct a 90% confidence interval to determine if there is a difference in the proportion of individuals who believe it is morally wrong for unwed women to have children. The lower bound is. (Round to three decimal places as needed.) The upper bound is. (Round to three decimal places as needed.) Because the confidence interval 0, there is evidence at the alpha = 0.05 level of significance to conclude that is a difference in the proportions. It seems that the proportion of individuals who earn over 4100, 000 that feel it is morally wrong for unwed women to have children's is the proportion of individuals who earn less than $100, 000 that feel it is morally wrong for unwed women to have children.Explanation / Answer
n1 = 1205
n2 = 1310
p1 = 0.593360996
p2 = 0.529007634
% = 95
Pooled Proportion, p = (n1 p1 + n2 p2)/(n1 + n2) = (1205 * 0.593360995850622 + 1310 * 0.529007633587786)/(1205 + 1310) = 0.559840954
q = 1 - p = 1 - 0.559840954274354 = 0.440159046
SE = (pq * ((1/n1) + (1/n2))) = (0.559840954274354 * 0.440159045725646 * ((1/1205) + (1/1310))) = 0.01981422
z- score = 1.959963985
Width of the confidence interval = z * SE = 1.95996398454005 * 0.0198142195961671 = 0.038835157
Lower Limit of the confidence interval = (p1 - p2) - width = 0.0643533622628362 - 0.0388351567902552 = 0.025518205
Upper Limit of the confidence interval = (p1 - p2) + width = 0.0643533622628362 + 0.0388351567902552 = 0.103188519
The 95% confidence interval is [0.026, 0.103]
Because the confidence interval excludes 0, there is sufficient evidence that there is a difference in the proportions.