A sample of n = 9 college students is used to evaluate the effectiveness of a new Study Skills Workshop.Each student's grade point average (GPA)is recorded for the semester before the workshop and for the semester after the workshop.The average GPA improved by MD = 0.60 points with s² = 0.09.The researcher would like to use the sample to estimate how much effect the workshop would have for the entire college population.Which of the following is the 80% confidence interval for these data?
A)µD = 0.60 + 0.01(1.397)
B)µD = 0.60 + 0.09(1.860)
C)µD = 0.60 + 0.10(1.397)
D)µD = 0.60 + 0.10(1.860)

Question

Quizplus · Accepted Answer

The formula for calculating the confidence interval for a population mean difference is:

CI = (MD - tα/2 *SEMD, MD + tα/2 *SEMD)

where 
MD = sample mean difference (0.60 in this case)
tα/2 = t-value for the level of confidence (80% confidence interval, so t-value from t-distribution table with df = n-1 = 8 and α/2 = 0.10)
SEMD = standard error of the mean difference

SEMD = s/√n = 0.09/√9 = 0.03

Plugging in the values, we get:

CI = (0.60 - 1.397*0.03, 0.60 + 1.397*0.03)
   = (0.55, 0.65)

Therefore, the 80% confidence interval for the population mean difference in GPA before and after the workshop is (0.55, 0.65).

Choice C is the closest option to this calculated interval.

A Sample of N = 9 College Students Is Used