In a sample of 14 participants,a researcher estimates the 90% CI for a sample with a mean of = 10.7 and an estimated standard error for the difference ( )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

In a sample of 14 participants,a researcher estimates the 90% CI for a sample with a mean of  = 10.7 and an estimated standard error for the difference (  )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.

Quizplus · Accepted Answer

We can use the formula for confidence interval: 
CI = mean ± (critical value) x (standard error)

Since the sample size is small (n=14), we need to use a t-distribution and find the critical value at the 90% level of confidence with 13 degrees of freedom (14-1):

t = 1.771

Then, we can plug in the values:

CI = 10.7 ± (1.771) x (2.9)
CI = 10.7 ± 5.14
CI = (10.7 - 5.14, 10.7 + 5.14)
CI = (5.56, 16.84)

Therefore, the 90% CI is 5.5 to 15.9, which is answer choice B.

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