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$\overline{ X }= 180.975$ 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 ± $116.621
B) $180.975 ± $94.066
C) $180.975 ± $119.586
D) $180.975 ± $99.123

Question

Quizplus · Accepted Answer

The 95% confidence interval is calculated using the formula: $\overline{X} \pm t^* \times \frac{s}{\sqrt{n}}$. With n = 8, the t-value for 95% confidence is approximately 2.3646. Thus, the interval is $180.975 \pm 2.3646 \times \frac{143.042}{\sqrt{8}}$, which equals $180.975 \pm 119.586$.

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

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