One of the editors of a major automobile publication has collected data on 30 of thebest-selling cars in the United States. The data are shown in the accompanying table. The editor is particularly interested in the relationship between highway mileage(miles pergallon) and curb weight of the vehicles. Complete parts a through c below. Use a significance level of 0.05 where needed

A. (1)Compute the correlation coefficient for the two variables and test to determine whether there is a linear relationship between the curb weight and the highway mileage of automobiles.

r= ___ (Round to three decimal places asneeded.)

(2)What are the appropriate hypotheses to test for a linearrelationship?

B. (1) Calculate thet-test statistic for correlation.

t=____ (Round to three decimal places asneeded.)

(2) Determine the criticalvalue(s) for the rejection region for the test statistic t. Select the correct choice below and fill in the answer box to complete your choice. Assume a significance level of 0.05 for the hypothesis test.

(3) Since the test statistic IS or IS NOT in the rejectionregion DO NOT REJECT or REJECT the null hypothesis. Conclude there IS or IS NOT a significant linear relationship between the curb weight and the highway mileage of automobiles.

c.(1) Compute the linear regression equation based on the sample data.

y=___ +(____)x

(2) A car weighs approximately 4,031 pounds. Provide an estimate of the average highway mileage expected to obtain from this model.

The expected highway mileage is ____ MPG

data:

Mileage,_Highway_MPG 30 28 30 31 29 31 30 29 29 26 25 23 26 27 23 20 22 24 23 19 19 20 19 22 22 24 29 22 20 23

Curb_Weight 3305 3356 3077 3046 3174 2924 3196 3195 3143 3293 3622 3886 3496 3662 3538 3917 3588 3232 3545 4703 4827 4541 4594 3059 3804 3353 3169 3444 3895 3177