In a sample of 14 participants,a researcher estimates the 90% CI for a sample with a mean of M₁ - M₂ = 10.7 and an estimated standard error for the difference (S_M1_-_M2)of 2.9.What is the confidence interval at this level of confidence? A) 90% CI 4.4, 17.0 B) 90% CI 5.5, 15.9 C) 90% CI 7.8, 13.6 D) There is not enough information to answer this question.

Question

Quizplus · Accepted Answer

Using the formula:

CI = (difference in means) ± (critical value) * (standard error)

We can calculate the critical value for a 90% confidence interval with 12 degrees of freedom (14 - 2) using a t-distribution table or calculator as approximately 1.782.

Plugging in the given values:

CI = 10.7 ± 1.782 * 2.9

CI = 10.7 ± 5.17

CI = (10.7 - 5.17, 10.7 + 5.17)

CI = (5.53, 16.87)

So the 90% confidence interval for the difference in means is (5.53, 16.87). Therefore, the answer is B: 90% CI 5.5, 15.9.

In a Sample of 14 Participants,a Researcher Estimates the 90