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:

The value of P-value is 0.0472.

Step-by-step 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\neq \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 \times 0.0236 = 0.0472

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


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