The research group asked the following question of individuals who earned in exc
ID: 3312496 • 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 wrong for unwed women to have children?" Of the 1205 individuals who earned in excess of $100,000 per year, 710 said yes of the 1310 individuals who earned less than $100,000 per year, 690 said yes. Construct a 95% 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 Round to three decimal places as needed) Because the confidence interval over $100,000 that feel it is morally wrong for unwed women to have children is | 0, there is evidence at the 0.05 level of significance to conclude that there is a difference in the proportions. It seems that the proportion of individuals who earn the proportion of individuals who earn less than $100 000 that feel it is morally wrong for unwed womento have childrenExplanation / Answer
p1 = 710/1205 = 0.589
p2 = 690/1310 = 0.527
Sample proportion P = (p1 * n1 + p2 * n2)/(n1 + n2)
= (0.589 * 1025 + 0.527 * 1310)/(1025 + 1310) = 0.554
SE = sqrt (P * (1 - P) * (1/n1 + 1/n2))
= sqrt (0.554 * 0.446 * (1/1025 + 1/1310))
= 0.021
The confidence interval is
p1 - p2 +/- z0.025 * SE
= 0.589 - 0.527 +/- 1.96 * 0.021
= 0.062 +/- 0.041
= 0.021, 0.103
Lower bound is 0.021
Upper bound is 0.103
Because the Confidence interval doesn't contain 0, there is sufficient evidence that there is a difference in proportion.
It seems that the proportion of individual who earn over $10000 that feel it is morally wrong for unwed women to have children is differ from the proportion of individual who earn less than$1000000 tht feel it is motally wrong for unwed women to have chi.