1. 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 18 private colleges in the United States provided a summary statistics yield = $180.975 and S = 143.042
2. What is the "t" Statistic for calculating a 99% Confidence Interval for the mean endowment of private colleges?
3. Calculate a 99% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments
4. You have summary demographic data on two Staten Island neighborhoods (Table 1). You also have some summary data on the final sale prices of homes in these two neighborhoods during the last year.
5. Use the information in the table below to construct a 99% confidence interval for Price per Square Foot for houses in Westerleigh
6. How many degrees of freedom will be used for the Confidence Interval?
7. What is the critical "T" or "Z" value for the test?
8. Test the Hypothesis that the Average Price Per Square Foot in Westerleigh is less than $325.00 (Be sure to state your Null and Alternate Hypotheses and conclusion in English)

Table 1

Summary Statistics

	Neighborhood	N	Averages	Std. Deviation	Std. Error Mean
Price Per Square Foot	Mariners Harbor	50	$305.79	$76.280	$10.788
	Westerleigh	22	$194.35	$50.879	$10.847
Living Space in House Square Feet	Mariners Harbor	50	1439.94	476.621	67.404
	Westerleigh	22	1954.64	419.440	89.425

1. The mean length of a small counterbalance bar is 43 millimeters. There is concern that the adjustments of the machine producing the bars have changed. Test the claim at the 0.02 level that there has been no change in the mean length. The alternate hypothesis is that there has been a change. Twenty-One (n = 21) were selected at random and their lengths were recorded. The mean of the sample is 42.5 and the standard deviation of 1.784.
2. State the Null and Alternate Hypotheses
3. Calculate the "t" and identify the critical "t" value.
4. Has there been a statistically significant change in the mean length of the bars?

4. Out of 1,050 randomly selected adults, 360 identified themselves as manual laborers, 280 identified themselves as non-manual wage earners, 250 identified themselves as mid-level managers and 160 identified themselves as executives. In the survey, 82% of manual laborers preferred trucks, 62% of non-manual wage earners preferred trucks, 54% of mid-level managers preferred trucks and 26% of executives preferred trucks.

1. 1. We are interested in finding the 95% confidence interval for the percent of executives who prefer trucks. Define random variables X and P in words.
   2. Which distribution should you use for this problem?
   3. Construct a 95% confidence interval. State the confidence interval