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# Basic statistics and hypothesis testing using Minitab

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Instructions:
? Follow the directions for each problem.
? Use Minitab for all the calculations.
? The data set is available in contents page of D2L in the Final Exam module called fall 2009.MTW.
? Label each printout of your Minitab session according to the problem and part of that problem.
? Use a separate sheet for each problem. Staple the sheets together in order with a coversheet that has your name and discussion section.
? Answer all the questions thoroughly, hand in both the answers to the questions and the Minitab printouts. You can cut and paste the Minitab output into Word if so desired.
? If there are any questions do not hesitate to ask your TA or instructor.
? This is to be your own work.
? Total possible points 50.

Problem 1: (10 points) The data is in the worksheet fall 2009.MTW. This worksheet contains the list Price, number of bedrooms (Bed), number of bathrooms (Bath), size (Sq Feet) and City that the house is in (Milwaukee or Madison) from a simple random sample of houses that are for sale.
a) What is the population? Be specific.
b) Construct a histogram of the square feet of these houses. Under binning tab for editing X-axis, use the cutpoint as the interval type, and use 10 classes (number of intervals) What "shape" is this histogram?
c) Give the mean, standard deviation, median, Q1 and Q3 for the square feet from this sample.

Problem 2: (5 points) Use the worksheet fall 2009.MTW. We want to estimate the mean list price of a home for sale.
a) Estimate the mean list price of all houses that are for sale in Milwaukee and Madison. Use a 99% confidence interval.
b) Interpret the 99% confidence interval found in part a.

Problem 3: (20 points) Again use the worksheet fall 2009.MTW. Is the mean list price for houses in Milwaukee less than the mean list price of houses in Madison? To answer this question we will construct a confidence interval and hypothesis test.

a) Find the sample mean list price for the houses that are for sale in Milwaukee and Madison separately. Hint: We want to determine the sample mean by the categorical variable City.
b) Create a boxplot of the list price by city. Give any similarities or differences to the list price between the two cities.
c) Determine a 98% confidence for the difference in the mean list price of homes for sale in Milwaukee and homes for sale in Madison. Use city as the subscript.
d) Let Madison be population 1 and Milwaukee be population 2. Test if mean list price for houses in Madison is greater than the mean list price of houses in Milwaukee. Give the null and alternative hypothesis, p-value, decision of the test and conclusion. Use a =0.05.

Problem 4: (15 points) Use the worksheet fall 2009.MTW. In most real estate markets the price of the home is directly related to the size of the house. We want to use the size of a house to predict the price of a home.

a) Give a scatterplot of price (y-axis) and square feet (x-axis). Describe the relationship between price and size by describing the form, direction and scatter of this scatterplot.
b) Determine the correlation between list price and size (sq feet).
c) Determine the simple linear regression line to predict list price by size (sq feet) of a house.
d) Using the regression equation, predict the list price of a home that has a size of 2,400 sq. feet.
e) What percent of variation in list price can be explained by this regression equation?