A random sample of 250 men yielded 175 who said they'd ridden a motorcycle at some time in their lives, while a similar sample of 215 women yielded only 43 who had done so. Find a 99% confidence interval for the difference between the proportions of men and women who have ridden motorcycles.

Question

A random sample of 250 men yielded 175 who said they'd ridden a motorcycle at some time in their lives, while a similar sample of 215 women yielded only 43 who had done so. Find a 99% confidence interval for the difference between the proportions of men and women who have ridden motorcycles.
0.5 plus/minus 0.103

0.5 plus/minus 0.078

.4688 plus/minus 0.085

5 plus/minus 0.085

0.5 plus/minus 0.112

GPT 3.5 · Answer

0.4688 plus/minus 0.085

Explanation:
First, calculate the proportions for men and women who have ridden motorcycles:
Proportion for men = 175/250 = 0.7
Proportion for women = 43/215 = 0.2

Now, find the standard error:
SE = sqrt((0.7*(1-0.7)/250) + (0.2*(1-0.2)/215)) = sqrt((0.00196) + (0.001355)) = sqrt(0.003315) = 0.05755

Find the margin of error for a 99% confidence interval with a z-score of 2.576:
Margin of error = 2.576 * 0.05755 = 0.14833

Now, calculate the confidence interval:
Lower bound = 0.7 - 0.2 - 0.14833 = 0.35167
Upper bound = 0.7 - 0.2 + 0.14833 = 0.84833

So, the 99% confidence interval for the difference between the proportions of men and women who have ridden motorcycles is 0.4688 plus/minus 0.085.