Question

A health policy economist interested in investigating the relationship between the cost of prescription drugs in Canada and the cost of prescription drugs in the United States has information from a random sample of

51

prescription drugs sold in both countries. For each of these drugs, the economist is examining two pieces of information: the average cost

x

(in Canadian dollars) of a one-month supply of the drug in Canada, and the average cost

y

(in U.S. dollars) of a one-month supply of the drug in the United States. Using computer software, the economist finds that, for the sample of drugs examined, the least-squares regression equation relating

x

and

y

is

y=−0.66+ 0.77x

. The economist also notices from the software that the standard error of the slope of the least-squares regression line is approximately

0.32

.

Test for a significant linear relationship between

x

and

y

by doing a hypothesis test regarding the population slope

β1

. (Assume that the variable

y

follows a normal distribution for each value of

x

and that the other regression assumptions are satisfied.) Use the

0.05

level of significance, and perform a two-tailed test. Then fill in the table below.

(If necessary, consult a list of formulas.)

The null hypothesis:	H0:
The alternative hypothesis:	H1:
The type of test statistic:	(Choose one)Z,t,Chi square, or F
The value of the test statistic: (Round to at least three decimal places.)
The two critical values at the 0.05 level of significance: (Round to at least three decimal places.)	and
Based on the data, can the economist conclude (using the 0.05 level) that there is a significant linear relationship between the average prescription drug cost in Canada and the average prescription drug cost in the United States?		Yes	No

Answer 1

The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: t The value of the test statistic: (Round to at least three decimal places.) 0.77/0.32 = 2.406 The two critical values at the 0.05 level of significance: (Round to at least three decimal places.)- -1.960,1.960 Based on the data, can the economist conclude (using the 0.05 level) that there is a significant linear relationship between the average prescription drug cost in Canada and the average prescription drug cost in the United States? yes