Private colleges and universities rely on money contributed by individuals and c

Question

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of tis moeny is put int 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 222.0. Summary statistics yield X-bar (aka the mean)= 180.975 and S = 143.042.

a.) 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.

b.) Calculate a 99% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments.

ANSWERS ARE GOOD, BUT PLEASE SHOW ME THE WORK SO I CAN FOLLOW ALONG

Explanation / Answer

(a) xBar = 180.975 sx = 143.0423 n = 8 the critical value of the t distribution with 7 degrees of freedom is 2.364624 (check student t table) the CI is: xBar ± t * sx / sqrt(n) $180.975 ± 2.364624 * 143.0423 / sqrt(8) $180.975 ± $119.586 ---------------------------------------------------------------------------------------------------- (b) the critical value of the t distribution with 7 degrees of freedom is 1.894579 (check student t table) So the CI is $180.975 ± 1.894579 * 143.0423 / sqrt(8) (85.16029, 276.7897)

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