A 95% confidence interval for the difference between two population means is found to be (−0.08, 0.15). Which of the following statements is true?
A)We can be 95% confident that the true difference between the population means falls between −0.08 and 0.15.
B)The probability is 0.95 that a significant difference between the population means lies between −0.08 and 0.15.
C)The probability is 0.05 that the true difference between the population means is between −0.08 and 0.15
D)The two populations cannot have the same means.

Question

Quizplus · Accepted Answer

A 95% confidence interval means that if we were to construct multiple confidence intervals from the same data, 95% of them would contain the true difference between the population means. Therefore, we can say with 95% confidence that the true difference falls between −0.08 and 0.15. Option A correctly conveys this interpretation. Option B is incorrect because the confidence interval provides information on a range of plausible differences, not on the probability of significant difference. Option C is incorrect because the probability that the true difference falls in the interval is 0.95, not 0.05. Option D is incorrect because we cannot conclude about the equality of population means based solely on a confidence interval.

A 95% Confidence Interval for the Difference Between Two Population