Question

Suppose that the mean annual temperature in Asheville has historically been 54.2 F. We take a sample of the last 10 years and use that to decide if there is evidence that the mean annual temperature has changed.

a. Write the null and alternative hypotheses for the hypothesis test you would perform.

b. Describe what the Type I and Type II errors would be in this situation.

Answer 1

(a) The null hypothesis is that the mean annual temperature in Asheville is equal to 54.2 F and the alternative hypothesis is that the mean annual temperature in Asheville is not equal to 54.2 F.

Symbolically,

H0: μ = 54.2 F

H1: μ ≠ 54.2 F

(b) Type I error would happen if we conclude that the mean annual temperature in Asheville is not equal to 54.2 F, when in fact, the mean annual temperature in Asheville is equal to 54.2 F.

Type II error would happen if we conclude that the mean annual temperature in Asheville is equal to 54.2 F, when in fact, the mean annual temperature in Asheville is not equal to 54.2 F.