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Making Inferences Based on a Single Sample

I. Explain what the phrase 95% confident means when we interpret a 95% confidence interval for mu.
a. In repeated sampling, 95% of similarly constructed intervals would contain the value of the population mean.
b. 95% of similarly constructed intervals would contain the value of the sampled mean.
c. 95% of the observations in the population fall within the bounds of the calculated interval.
d. The probability that the mean falls in the calculated interval is 0.95.
e. None of the above.

II. Find z(alpha/2) for alpha = 0.06.
a. 1.88
b. 1.645
c. 1.96
d. 2.33
e. None of the above.

III. 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): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. Summary statistics yield a sample mean of 180.975 and a standard deviation of 143.042. Calculate a 99% confidence interval for the mean endowment of all private colleges in the United States. The best answer below is:
a. 180.975 ± 181.387 Note: ≠ symbolizes + or -.
b. 180.975 ± 176.955
c. 180.975 ± 169.672
d. 180.975 ± 189.173

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