THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A dependent random sample from two normally distributed populations gives the following results:
n = 20,
= 26.5,s₂ = 3.2
-A 95% confidence interval estimate for the difference between two population means,μ₁ - μ₂,is determined to be 62.75 < μ₁ - μ₂ < 68.52.Which of the following is true if the confidence level is reduced to 90%?

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A dependent random sample from two normally distributed populations gives the following results: n = 20, = 26.5,s 2 = 3.2 -A 95% confidence interval estimate for the difference between two population means,μ₁ - μ₂,is determined to be 62.75 < μ₁ - μ₂ < 68.52.Which of the following is true if the confidence level is reduced to 90%? A)The confidence interval becomes wider. B)The confidence interval remains the same. C)The confidence interval becomes narrower. D)More information is required to determine the answer.

Quizplus · Accepted Answer

When the confidence level is reduced, the confidence interval becomes narrower because a lower confidence level means accepting a higher probability of error, thus requiring a smaller range to capture the true parameter with the specified level of confidence.