Write the word or phrase that best completes each statement or answers the question.
Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected
-x1 = 59, n1 = 117 and x2 = 68, n2 = 119; Construct a 98% confidence interval for the difference between population proportions p1 - p2.
A) -0.194

Question

Write the word or phrase that best completes each statement or answers the question.
Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected
-x1 = 59, n1 = 117 and x2 = 68, n2 = 119; Construct a 98% confidence interval for the difference between population proportions p1 - p2.
A) -0.194 < p1 - p2 < 0.631
B) 0.377 < p1 - p2 < 0.631
C) -0.218 < p1 - p2 < 0.084
D) 0.353 < p1 - p2 < 0.655

Quizplus · Accepted Answer

We can use the formula for the confidence interval for the difference between two population proportions:
(p1 - p2) ± z*sqrt((p1q1/n1) + (p2q2/n2))
where p1 and p2 are the sample proportions, q1 and q2 are the complements of p1 and p2, n1 and n2 are the sample sizes, and z is the z-score corresponding to the desired confidence level. With a 98% confidence level, the z-score is 2.33. Plugging in the given values:
(59/117 - 68/119) ± 2.33*sqrt(((59/117)*(58/117)/117) + ((68/119)*(51/119)/119))
=-0.218 < p1 - p2 < 0.084. Therefore, the best choice is C.

Write the Word or Phrase That Best Completes Each Statement