Question

For each of the following research scenarios, give the appropriate sampling distribution (i.e., test statistic) and indicate the appropriate statistical procedure to test the null hypothesis, and state the most appropriate null and alternate hypotheses

House sales price is known to be highly influenced by location. An urban geographer believes that suburban houses within walking distance (<1.5 km) of transit hubs such as rail or subway stations will be more attractive and thus more expensive than similar sized houses more than 2k from transit hubs. To test this, sales data (final sale price) were collected for similar sized houses that fit these characteristics.

Answer 1

As we are testing here whether  suburban houses within walking distance (<1.5 km) of transit hubs such as rail or subway stations will be more attractive and thus more expensive than similar sized houses more than 2k from transit hubs, therefore this is a two sample test for comparing the mean prices for the houses at the two locations. Let the mean price for houses within walking distance (<1.5 km) of transit hubs such as rail or subway stations be the first set of prices, while those similar sized houses more than 2k from transit hubsbe the second set of prizes, then the null and the alternative hypothesis here are given as:

The type of sampling required here is a random sampling technique. Also the test statistic here is computed as:

Where s_d is the sample size and is the mean of difference in the prices of the two sets of prices.