Question: Real Estate and Real t-tests

The sales price of a home certainly depends on its size and, of course, larger homes generally receive a higher price. How much can we learn about a house from the fact that it has a fireplace or more than the average number of bedrooms?

From a larger data set of over one thousand homes from the upstate New York area, two random samples of 50 listings each have been extracted. One sample has houses with fireplaces and the other has houses without fireplaces. The spreadsheet also has: Price ($), Living Area (sq ft), and Age (years) for each listing. See the RealEstate worksheet of the data spreadsheet.

1. Carry out three hypothesis tests to see whether there is a real difference in mean price, mean living area, and mean age of these two populations.
   Do only the first test, of mean price, manually and show the details of your hypothesis test for the mean price. For the other two tests you may use Excel and you do not need to report the details; just report the hypotheses, value of the test statistic, and conclusion.
   Note: The level of significance is not specified. Draw your conclusions by referring to the strength of evidence indicated by the p-value. Hint: Remember the three alpha values most commonly used: 0.10 = moderate, 0.05 = strong, 0.01 = very strong.
2. For the difference in mean house prices, find a 90% confidence interval.
3. Give one sentence to describe how the first hypothesis test in part b) and the confidence interval in part c) reflect the relationship between confidence intervals and hypothesis tests.

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