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Question 6 • Statistics

The daily temperatures in fall and winter months in Virginia have a mean of 62 times degree F A meteorologist in southwest Virginia believes the mean temperature is colder in this area. The meteorologist takes a random sample of 15 daily temperatures from the fall and winter months over the last five years in southwest Virginia. The mean temperature for the sample is 58 times degree F with a standard deviation of 4 point 1 2 times degree F A significance test at an alpha level of α=0.05 produces a cap p -value of 0 point 0 0 1 What is the correct interpretation of the cap p -value?

Answer
A
There is a 0 point 1 percent probability that a sample mean temperature of 58 times degree F will occur by chance alone if the true mean temperature is 62 times degree F .
B
Assuming the true mean temperature is 62 times degree F , there is a 99 point 9 percent probability that a sample mean of 58 times degree F will occur by chance alone.
C
Assuming the true mean temperature is 62 times degree F , there is a 0 point 1 percent probability that the null hypothesis is true by chance alone.
D
There is a 0 point 1 percent chance that a sample mean temperature of at most 58 times degree F will occur by chance if the true mean temperature is 62 times degree F .

Explanation

The p-value is the probability, assuming the null hypothesis is true (the mean temperature is 62°F), of getting a sample result at least as extreme as the observed result in the direction of the alternative. Because the meteorologist is testing whether temperatures are colder, the relevant results are sample means of 58°F or lower. A p-value of 0.001 is a 0.1% chance of such a result, so D is correct.

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