Part A:
The sample mean is at the midpoint of the lower and the upper values of the confidence interval.
Thus, the sample mean is given by:
(77 + 65) / 2 = 71
Therefore, the sample mean is 71.
Part 2:
The margin of error is the distance between the upper and the lower confidence interval values from the sample mean.
Thus, margin of error is given by 77 - 71 = 71 - 65 = 6.
Therefore, margin of error is 6.
Part 3:
The margin of error is given by
where
is the value of the t-distribution given the degree of freedom; s is the sample standard deviation and n is the sample size.
Since the sample size is 25, the degree of freedom is 25 - 1 = 24.
From the t-distrbution table, we have:
Thus, margin of error is given by: