Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses.Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund.A recent survey of 8 private colleges in the United States revealed the following endowments (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 endowment of all the private colleges in the United States assuming a normal distribution for the endowments.
A)$180.975 $\pm$ $94.066
B)$180.975 $\pm$ $99.123
C)$180.975 $\pm$ $116.621
D)$180.975 $\pm$ $119.586

Question

Quizplus · Accepted Answer

The 95% confidence interval is calculated using the formula: $\bar{X} \pm t^* \frac{S}{\sqrt{n}}$, where $t^*$ is the t-value for 95% confidence with $n-1$ degrees of freedom. Using the given data, the interval is approximately $180.975 \pm 119.586$.

Private Colleges and Universities Rely on Money Contributed by Individuals Xˉ=180.975\bar { X } = 180.975Xˉ=180.975

Private Colleges and Universities Rely on Money Contributed by Individuals $\bar { X } = 180.975$