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?

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 [tex]\mu_1[/tex] = true average price of apartments in town A

[tex]\mu_2[/tex] = true average price of apartments in town B

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex]

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex]

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( [tex]t__n__1+_n_2-_2[/tex] > 2.1)

= P( [tex]t_2_5[/tex] > 2.1) = 0.0236

In two-tailed test, P-value is calculated as = 2 [tex]\times[/tex] 0.0236 = 0.0472

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