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 30 daily temperatures from the fall and winter months over the last five years in southwest Virginia. The mean temperature for the sample is 59 times degree F with a standard deviation of 6 point 2 1 times degree F Do the data provide convincing evidence at the alpha is equal to 0 point 0 5 level that the mean temperature in fall and winter months in southwest Virginia is less than 62 times degree F ? What is the test statistic for this significance test?
Answer
A
t is equal to 2 point 6 5
B
t is equal to negative 2 point 6 5
C
z is equal to negative 2 point 6 5
D
z is equal to 2 point 6 5
Explanation
Use a one-sample t statistic because the population standard deviation is unknown and the sample standard deviation is given. Calculate t = (59 − 62) / (6.21 / √30) ≈ −2.65. The negative value fits the sample mean being below 62°F, so the test statistic is t = −2.65, choice B.
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