Question

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 eight private colleges in the United States revealed the following endowments (in millions of dollars): 87, 40, 275, 120, 200, 110, 500, and 200.  What value will be used as the point estimate for the mean endowment of all private colleges in the United States?

Answer 1

We have to obtain a point estimate for the mean endowment of all private colleges in the United States.

We know that, the sample mean is the best (unbiased) estimate of population mean. Therefore, considering the recent survey as the sample (Observations x_i (say)), the sample mean can be computed using the formula:

Hence, sample mean 191.5 million dollars will be used as the point estimate for the mean endowment of all private colleges in the United State.

(*However, the sample size is too small (n=8) to be reliable. A mean of a larger sample would yield a closer and more accurate point estimate, as it would be a better representation of the population.)