Question

You wish to compare the prices of apartments in two neighboring towns. You take a simple random sample of 12 apartments in town A and calculate the average price of these apartments. You repeat this for 15 apartments in town B. Let \mu_1μ 1 represent the true average price of apartments in town A and \mu_2μ 2 the average price in town B.Suppose we were to use the two-sample t test and found that the t statistic for comparing the mean prices is 2.1. What can we say about the value of the p-value?

Answer 1

The value of P-value is 0.0472.

Explanation:

We are given that you take a simple random sample of 12 apartments in town A and calculate the average price of these apartments. You repeat this for 15 apartments in town B.

Let
`\mu_1` = true average price of apartments in town A

`\mu_2` = true average price of apartments in town B

So, Null Hypothesis,
`H_0` :
`\mu_1=\mu_2`

Alternate Hypothesis,
`H_A` :
`\mu_1\\eq \mu_2`

The test statistics that have been used here is two-sample t-test statistics, i.e;

The test statistics given to us is 2.1

Now, the P-value of the test statistics is given by the following formula;

P-value = P(
`t__n__1+_n_2-_2` > 2.1)

= P(
`t_2_5` > 2.1) = 0.0236

In two-tailed test, P-value is calculated as = 2
`*` 0.0236 = 0.0472

Hence, the value of the p-value is 0.0472.