Business Statistics

ECON 2110

Dr. Martin Gritsch

Assignment 2

A reminder about Academic Integrity from the syllabus:

Cheating in its various forms will be severely punished. The minimum penalty is a grade of zero on the assignment in question, but it can go up to expulsion from the university. If you have not done so yet, please familiarize yourself with the “Academic Integrity Policy” (available online at http://www.wpunj.edu/dotAsset/230122.pdf). All parts of that Policy are relevant and important, but for the online setting of the class, I especially would like to stress sections II.B. (on plagiarism) and II.C. (on collusion).

Please make sure that you truly understand what all parts of the policy mean. To name a few examples, working together with another student on an assignment, getting help on an assignment from someone else (e.g., a tutor), and copying another student’s work are all violations of the Academic Integrity Policy.

Someone claims that houses with a garage on average sell for less than houses without a garage. That strikes you as odd, so you collect a sample of selling prices of houses to test that claim. The sample includes 71 houses with garage and 34 houses without garage.

Please note that all the prices given are in thousands of dollars. I only mention this for the numbers to make sense and do not recommend doing any conversions. Instead, please just use the values as they are.

The mean selling price of the houses with garage is 238.2 with a sample variance of 2,013.9.

The mean selling price of the houses without garage is 185.5 with a sample variance of 784.3.

Part (a) (2 points)

As you can see, the data do not seem to support the claim that houses with a garage on average sell for less than houses without a garage. Explain why it is still necessary to carry out a hypothesis test.

Part (b) (3 points)

We will return to this point later, but for the time being, please choose your test statistic assume that the population variances are not equal to each other nor are they known. That technically makes the t-distribution the appropriate distribution, but since we have large(-ish) samples, feel free to use the standard normal distribution.

Denote the population mean of houses with garage as µ1 and the population mean of houses without a garage as µ2. Using a significance level of 0.05, carry out a hypothesis test for:

H0: µ1 ≤ µ2

H1: µ1 > µ2