Private colleges rely on money contributed by individuals for much of their major building expenses.Much of this money is put into a fund called a trust,and the college spends only the interest earned by the fund.A recent survey of 8 private colleges in Australia revealed the following trusts (in millions of dollars): 60.2,47.0,235.1,490.0,122.6,177.5,95.4,and 220.0.Summary statistics yield $\bar { X }$ = 180.975 and S = 143.042.Calculate a 95% confidence interval for the mean trust of all the private colleges in Australia assuming a normal distribution for the trusts.
A) $180.975 ± $99.123
B) $180.975 ± $119.586
C) $180.975 ± $116.621
D) $180.975 ± $94.066

Question

Quizplus · Accepted Answer

We are given the sample mean (x̄) and the sample standard deviation (S). 
Using a t-distribution with n-1 degrees of freedom (n=8), we can calculate the margin of error:
t_critical = 2.306 (for a 95% confidence interval and 7 degrees of freedom)
Margin of error = t_critical * (S/√n) = 2.306 * (143.042/√8) = 99.586
Therefore, the 95% confidence interval is:
x̄ ± margin of error = 180.975 ± 99.123
So the answer is B.

Private Colleges Rely on Money Contributed by Individuals for Much Xˉ\bar { X }Xˉ

Private Colleges Rely on Money Contributed by Individuals for Much $\bar { X }$