Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is invested in a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 48 private colleges in the United States revealed the following endowments (in millions of dollars):
145.8186.5127.3317.28.4214.885.2277.1140.1338.9
180.772.9210.1425.143.6471.684360.5380.7219.2
378.8390.652.4245.9285.534.3127.5221.741.25.5
10.5146.6200.9305.5234.9129.6161.9112.6164.263
44.9340.1114.9176.6635.399.2202.2116.4
Summary statistics yield the sample mean 194.43 millions of dollars and the sample standard deviation 136.55 millions of dollars. Construct and interpret a 90% confidence interval for the mean endowment of all private colleges in the United States. You may assume that the sample is from a normal population.
 
Procedure:
  1. Assumptions: (select everything that applies)
  2. Unknown parameter:
  3. Point estimate: =millions of dollars (Round the answer to 2 decimal places)
  4. Confidence level % and α=\displaystyle \alpha= , also
    •  α2=\displaystyle \frac{\alpha}{{2}}= , and 1α2=\displaystyle {1}-\frac{\alpha}{{2}}=
    • Critical values: (Round the answer to 3 decimal places)
      • left= right=
  5. Margin of error (if applicable): (Round the answer to 2 decimal places)
  6. Lower bound: (Round the answer to 2 decimal places)
  7. Upper bound: (Round the answer to 2 decimal places)
  8. Confidence interval:(, )
  9. Interpretation: We are % confident that the mean endowment of all private colleges in the United States is between millions of dollars and millions of dollars.
Based on the confidence interval, is it reasonable to believe that the mean endowment of all private colleges in the United States is greater than 173 millions of dollars? Explain.
, because 173 millions of dollars.