You wish to compare the prices of apartments in two neighboring towns. You take

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 1 represent the true average price of apartments in town A and 2 the average price in town B. Suppose we were to use the unpooled t test with the conservative estimate for the degrees of freedom. The t statistic for comparing the mean prices is 2.1. What can we say about the value of the P-value?

P-value < 0.01

0.05 < P-value < 0.10

P-value > 0.10

Explanation / Answer

this is unpooled test, hence conservative approach to use degrees of freedom is minimum of n1- 1 or n2 - 1

n1 - 1 = 12 - 1 = 11

n2 -1 = 15 - 1 = 14

Hence Df = 11

If we calculated the p-value for t-value = 2.1 with 11 degrees of freedom it comes as 0.0596

Note: this is two tailed test hence p-value = 2*P(t > 2.1)

Hence 0.05 < P-value < 0.10

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