Question

the plot shows a negative linear relationship between the latitude of the state and melanoma mortality rate. based on the scatterplot and the value of the correlation coefficient, it would make sense to test the significance of this observed linear relationship between latitude and melanoma mortality rate. which of the following are the appropriate null and alternative hypotheses? a. $h_0$: melanoma mortality rate is related to latitude. $h_a$: melanoma mortality rate is not related to latitude. b. $h_0$: melanoma mortality rate is not related to latitude. $h_a$: melanoma mortality rate is related to latitude. c. $h_0$: melanoma mortality rate is linearly related to latitude. $h_a$: melanoma mortality rate is not linearly related to latitude. d. $h_0$: melanoma mortality rate is not linearly related to latitude. $h_a$: melanoma mortality rate is linearly related to latitude.

Explanation:

In hypothesis testing for a linear relationship, the null hypothesis (\(H_0\)) typically assumes no linear relationship. The alternative hypothesis (\(H_a\)) is what we are trying to find evidence for, which in this case is a linear relationship. Options A and B do not specify "linear" which is relevant based on the problem context (mention of a linear relationship in the plot description). Option C has the null and alternative reversed.

Answer:

D. \(H_0\): Melanoma mortality rate is not linearly related to latitude. \(H_a\): Melanoma mortality rate is linearly related to latitude.