Exam 2 take home questions

Note: since this is part of exam 2, you are to work individually on these problems.   Do not discuss these questions with anyone except Dr. Williams.  Work each problem on a separate page, bring the take home problems (and all intermediate calculations) with you to the in-class exam on Friday, April 3.  One or more of these problems will be handed in with the in-class exam, and information from others will be used on some of the in-class questions.

1. A guitar store only sells guitars made by three companies: Gibson, Ibanez, and Taylor.  A separate random sample was taken of the guitars for sale from each company.  Use this information to calculate an estimate of the average guitar price at the store, and an error bound for your estimate.  What sample size should we take in a future sample (and how would we allocate it among companies) to achieve an error bound of $200?     

 2. A random sample of 59 houses was collected from the houses listed for sale in the Boise, Idaho area.  The data file contains the listed price for each house as well as the square footage of the house.  The mean square footage of all 20,000 houses for sale is 2524 square feet. From this data use simple random sampling, ratio, and regression estimators to estimate the average listing price for houses in the Boise area.  Create a scatterplot of the data and calculate an error bound for each estimator.     

 3. A systematic random sample was taken from the set of all Presidents of the United States.  The random sample shown below includes the height (in inches) of each sampled President. 

Martin Van Buren 	56.0 	
William McKinley 	57.0 	
William Henry Harrison 	68.0 	
Jimmy Carter 		69.0 	
Theodore Roosevelt 	70.0 	
Grover Cleveland 	71.0 	
James Buchanan 		72.0 	
John F. Kennedy 	72.0 	
Andrew Jackson 		73.0 	
George H.W. Bush 	74.0 	
Abraham Lincoln 	76.0

a) From this data, estimate the average height of United States Presidents.   Calculate two error bounds for your estimate, one using the usual SRS formula, and one using the successive difference variance estimator.

b) Which variance estimator is more appropriate for these data? 

4. For the housing data in problem 2, can you think of a way to design a future sampling study to have a lower error bound?   (For example, how could more information be used?)