In a sample of 17 participants,a researcher estimates the 90% CI for a sample with a mean of = 7 and an estimated standard error for the difference scores ( )of 2.2.What is the confidence interval at this level of confidence?
A)90% CI 2.4,11.6
B)90% CI 3.2,10.8
C)90% CI 4.8,9.2
D)There is not enough information to answer this question.

Question

In a sample of 17 participants,a researcher estimates the 90% CI for a sample with a mean of  = 7 and an estimated standard error for the difference scores (  )of 2.2.What is the confidence interval at this level of confidence?
A)90% CI 2.4,11.6 
B)90% CI 3.2,10.8 
C)90% CI 4.8,9.2 
D)There is not enough information to answer this question.

Quizplus · Accepted Answer

The formula for calculating the confidence interval for the mean is:

CI = X̄ ± (t_critical * SE)
where X̄ is the sample mean, t_critical is the critical t-value from the t-distribution table with n-1 degrees of freedom and the desired level of confidence, and SE is the estimated standard error of the mean.

Here, X̄ = 7, SE = 2.2, n = 17, and the desired level of confidence is 90%. From the t-distribution table with 16 degrees of freedom and a 90% level of confidence, the t_critical value is 1.745.

Plugging in the values, we get:

CI = 7 ± (1.745 * 2.2)
CI = 7 ± 3.84
CI = (7-3.84, 7+3.84)
CI = (3.16, 10.84)

Therefore, the 90% confidence interval is (3.2, 10.8), which is closest to choice B.

In a Sample of 17 Participants,a Researcher Estimates the 90