Explain 95% confidence interval for the population mean.
1. Private colleges as well as universities rely on money contributed by individuals and corporations for their operating expenses. Much of this funds is put into 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 220.0. Summary statistics yield = 180.975 and s = 143.042. Compute a 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments.
a) $180.975± $94.066
b) $180.975± $99.123
c) $180.975± $116.621
d) $180.975± $119.586
2. An economist is interested in reading the incomes of consumers in a particular region. The population standard deviation is known to be $1000. An arbitrary sample of 50 individuals resulted in an average income of $15,000. Explain what is the width of the 90% confidence interval?
a) $232.60
b) $364.30
c) $465.23
d) $728.60