Answer:
CI = (-0.0445, 0.0225)
there is no sufficient evidence to men and women have equal success in challenging calls
Step-by-step explanation:
Sample size for men; n1 = 1425
Number of success for men; x1 = 412
Sample size for women; n2 = 739
Number of success for women; x2 = 221
Significance level; α = 0.05
Sample proportion for men;
p1 = x1/n1 = 412/1425
p1 = 0.2891
Sample proportion for women;
p2 = x2/n2 = 221/739
p2 = 0.2991
From tables, z-score at significance level of 0.05 is 1.96.
Formula for margin of error is;
E = z√[(p1(1 - p1)/n1) + (p2(1 - p2)/n2)]
Plugging in the relevant values;
E = 1.96√[(0.2891(1 - 0.2891)/1425) + (0.2991(1 - 0.2991)/1425)]
E = 1.96 × 0.0170687
E = 0.0335
Coordinates of the confidence interval will be;
[(p1 - p2) - E], [(p1 - p2) + E]
[(0.2881 - 0.2991) - 0.0335], [(0.2881 - 0.2991) + 0.0335]
CI = (-0.0445, 0.0225)
This means that the confidence interval contains 0 since it's between (-0.0445 and 0.0225). Thus we can conclude that there is no sufficient evidence to men and women have equal success in challenging calls
