the gpa of 15 randomy slected students are shown below on this table.
2.87, 3.35, 3.61, 4.00, 3.73, 2.95, 3.02, 3.46, 3.21, 3.50, 3.89, 3.20, 3.62, 2.77, 3.92
construct a 95% confedence interval using a t-distribution for the mean gpa?
would agiven mean gpa of 3.72 be likly given the calculated confednce interval?
Solution
You have a sample of n=15, with a mean of 3.41 and a standard deviation of 0.395. The formula
for a confidence interval is:
Mean ± t/2 * st. dev. / n
where t/2 is a critical value of the t-distribution with n-1=15-1=14 degrees of freedom. In this
case, that number is 2.14. So the confidence interval is:
3.41 ± 2.14 * 0.395 / 15
3.41 ± 0.22
So from 3.19 to 3.63.
Given that 3.72 is outside this confidence interval, it is unlikely to be the mean.