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 490 men taken by the commissioner's office showed that 150 of them play the lottery often. Another sample of 315 women showed that 69 of them play the lottery often. Let p, be the proportion of men who play the lottery often, and p2 be the proportion of women who play the lottery often. a. What is the point estimate of the difference between the two population proportions? Round your answer to two decimal places. Point estimate of p, – P2 b. Construct a 99% confidence interval for the difference between the proportions of all men and all women who play the lottery often. Round your answers to two decimal places. to i c. Testing at a 10% significance level, can you conclude that the proportions of all men and all women who play the lottery often are different?

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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 490 men taken by the commissioner's office showed that 150 of them play the lottery often. Another sample of 315 women showed that 69 of them play the lottery often.

Let \( p_1 \) be the proportion of men who play the lottery often, and \( p_2 \) be the proportion of women who play the lottery often.

a. What is the point estimate of the difference between the two population proportions?

Round your answer to two decimal places.

Point estimate of \( p_1 - p_2 = \) [Input Box]

b. Construct a 99% confidence interval for the difference between the proportions of all men and all women who play the lottery often.

Round your answers to two decimal places.

[Input Box] to [Input Box]

c. Testing at a 10% significance level, can you conclude that the proportions of all men and all women who play the lottery often are different?
Transcribed Image Text: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 490 men taken by the commissioner's office showed that 150 of them play the lottery often. Another sample of 315 women showed that 69 of them play the lottery often. Let \( p_1 \) be the proportion of men who play the lottery often, and \( p_2 \) be the proportion of women who play the lottery often. a. What is the point estimate of the difference between the two population proportions? Round your answer to two decimal places. Point estimate of \( p_1 - p_2 = \) [Input Box] b. Construct a 99% confidence interval for the difference between the proportions of all men and all women who play the lottery often. Round your answers to two decimal places. [Input Box] to [Input Box] c. Testing at a 10% significance level, can you conclude that the proportions of all men and all women who play the lottery often are different?
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