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.

Answer 1

Explanation:

Given that private colleges and universities rely on money contributed by individuals and corporations for their operating expenses

A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars)

Mean = 180.975 and std dev s = 143.042

Assuming a normal distribution we have 95% critical value is 1.96 and 99% critical value is 2.58

a) 95% Conf interval = Mean ±1.96* std error

=
`(180.975-1.96((143.042)/(√(8) ) ,180.975+1.96((143.042)/(√(8) ))\\= (81.851, 280.098)`

Since sample size is very small confidence interval is wider.

b) 99% Conf interval = Mean ±2.58* std error

=
`(180.975-2.58((143.042)/(√(8) ) ,180.975+2.58((143.042)/(√(8) ))\\= (50.50,311.45)`

Since sample size is very small confidence interval is wider.