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Are men and women equally likely to be frequent binge drinkers? Let p1 be the proportion...

Are men and women equally likely to be frequent binge drinkers? Let p1 be the proportion of binge drinkers in men and p2 be the proportion in women.The following is the summary of a survey on this problem.

Group Sample size Number of binge drinkers

1(Men) 7180 1630

2(Women) 9916 1684

_____________________________________

Combined 17,096 3314

Estimate p1 − p2 based on the data, report the standard error for this estimate and a 95% confidence interval.

Math   Statistics-And-Probability   
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Answer #1

n1= 7180, x1= 1630

n2= 9916, x2 = 1684

formula for standard error is

Where Zc is z critical value for C= 95%

Zc= 1.96

Standard error = 0.0062183909

now formula for confidence interval is

0.045 < P1 - P2 < 0.069

Thus we get confidence interval as ( 0.045 , 0.069 )

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