Question

1. Endowment funds. Operating expenses in U.S. private and public colleges are funded through individual, corporation, and foundation contributions (a.k.a. donations). Much of this money is put into an endowment fund, and the college spends only the interest earned by the fund. A random sample of sixteen college endowments was drawn from the list of endowments in the Chronicle of Higher Education Almanac (Sept. 2, 1996). The endowments (in millions of dollars) were recorded and are ready to be analyzed.

Mean 625.78625

Std Dev 106.82618

N 16

Variance 11411.834

Minimum 420.44

Maximum 835.33

Median 614.65

Range 414.89

Interquartile Range 110.4975

Your task is to construct a 98% confidence interval for the true mean endowment amount, using the sample collected.

Answer 1

The provided sample mean is 625.78625 and the sample standard deviation is s = 106.82618 . The size of the sample is n = 16 and the required confidence level is 98%.

The number of degrees of freedom are df = 16 - 1 = 15 , and the significance level is α=0.02.

Based on the provided information, the critical t-value for α=0.02 and df = 15 degrees of freedom is t_c = 2.602 .

The 98% confidence for the population mean μ is computed using the following expression

  

Therefore, based on the information provided, the 98 % confidence for the population mean μ is

which completes the calculation.