Question

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A university financial aid office polled a random sample of 591 male undergraduate students and 484 female undergraduate students. Each of the students was asked whether or not they were employed during the previous summer. 424424 of the male students and 385 of the female students said that they had worked during the previous summer. Give a 95% confidence interval for the difference between the proportions of male and female students who were employed during the summer. Find the point estimate. Then, the margin of error. Finally, construct the 95% confidence interval. Round your answers to three decimal places.

Explaination: In the previous steps, we determined that the point estimate for the given information is pˆ1−pˆ2=−0.078p^1−p^2=−0.078 and the margin of error is E=0.051113E=0.051113. To determine the confidence interval, we must find the lower endpoint and the upper endpoint, rounding the values to three decimal places.

Lower endpoint:  pˆ1−pˆ2−E=−0.078−0.051113≈−0.129Upper endpoint:  pˆ1−pˆ2+E=−0.078+0.051113≈−0.027

ANSWERS

Point Estimate = −0.078

Margin of Error = 0.051113

Lower endpoint: −0.129, Upper endpoint: −0.027

Answer 1