Question: The lottery commissioner's office in a state wanted to find if the percentages of men and women who play the lottery often are different. A sample of 500 men taken by the commissioner's office showed that 160 of them play the lottery often. Another sample of 300 women showed that 66 of them play the lottery often.
a. What is the point estimate of the difference between the two population proportions?
b. Construct a 99% confidence interval for the difference between the proportions of all men and all women who play the lottery often.
c. Testing at the 1% significance level, can you conclude that the proportions of all men and all women who play the lottery often are different?