A survey of randomly chosen adults found that 38 of the 61 women and 46 of the 83 men follow regular exercise programs.Construct a 95% confidence interval for the difference in the proportions of women and men who have regular exercise programs.
A)(-0.124, 0.786)
B)(-0.093, 0.231)
C)(-0.124, 0.815)
D)(0.460, 0.786)
E)(0.430, 0.815)

Question

Quizplus · Accepted Answer

The confidence interval for the difference between two proportions is calculated using the formula for the standard error of the difference between two proportions and the Z-score for the desired confidence level (in this case, 95%, which corresponds to a Z-score of approximately 1.96). The proportions of women and men who follow regular exercise programs are 38/61 and 46/83, respectively. The calculation involves finding the difference between these two proportions and then computing the confidence interval using the standard error of the difference. The correct interval, which accounts for the variability in proportions and the sample sizes, is (-0.093, 0.231), indicating that the true difference in proportions could range from -0.093 to 0.231 with 95% confidence.

A Survey of Randomly Chosen Adults Found That 38 of the 61