Here Are the Rents for the One-Bedroom Apartments

Quiz 11.2A AP Statistics Name:

Pat wants to compare the cost of one- and two-bedroom apartments in the area of her college campus. She collects data for a random sample of 10 advertisements of each type. Here are the rents for the two-bedroom apartments (in dollars per month):

595, 500, 580, 650, 675, 675, 750, 500, 495, 670

Here are the rents for the one-bedroom apartments:

500, 650, 600, 505, 450, 550, 515, 495, 650, 395

1. Pat wonders if two-bedroom apartments rent for significantly more than one-bedroom apartments. Perform a significance test to answer her question. Follow the Inference Toolbox.

Step:1:

μ1 = mean rent for two-bedroom apartment

μ2 = mean rent for one-bedroom apartment

Ho: μ1 = μ2 same mean rent for both 1 & 2 bedroom apartments

Ha: μ1 < μ2 mean rent for 1 bedroom less than 2 bedroom apartments

Step 2: (2-sample t-test)

Conditions/Assumptions:

1.  SRS from ads may not be SRS from whole population, may not be independent since may come from same apt complex.

2.  Some skewedness in both graphs – no outliers, both normal probability plots non-linear

Due to the uncertainty of the conditions not being met, we will proceed with caution. Our conclusions may not be indicative of the whole population.

Step 3:

Step 4:

The chance of getting a 2 sample mean that differs as much as ours does is 2.9%, given Ho is true.

Given a p-value of .029, we would reject the null hypothesis.

We have evidence that two-bedroom apartments are more expensive than one-bedroom apartments.

2. Find a 95% confidence interval for the additional cost of a second bedroom. Interpret your interval in the context of this problem.

Step 4:

We are 95% confident that the actual difference in the mean rent for one-bedroom and 2-bedroom apartments is between -$2.94 and $158.94.

Chapter 11 Quiz 11.2A