DATAfile:MLBPitchingA statistical program is recommended. You may need to use the appropriatetechnologyto answer this question.In baseball, an earned run is any run that the opposing team scores off the pitcher except for runs scored as a result of errors. The earned run average (ERA), the statistic most often used to compare the performance of pitchers, is computed as follows.

ERA =

earned runs given up

innings pitched

9

Note that the average number of earned runs per inning pitched is multiplied by nine, the number of innings in a regulation game. Thus, ERA represents the average number of runs the pitcher gives up per nine innings. For instance, in 2008, Roy Halladay, a pitcher for the Toronto Blue Jays, pitched 246 innings and gave up 76 earned runs; his ERA was

76

246

9 = 2.78.

To investigate the relationship between ERA and other measures of pitching performance, data for 50 Major League Baseball pitchers for the 2008 season appear in the data set named MLBPitching, linked above. (Note: the values in the last three columns in the data set have been rounded for display, but exact values should be used for all calculations.)Descriptions for variables which appear on the data set follow.

W	Number of games won
L	Number of games lost
WPCT	Percentage of games won
H/9	Average number of hits given up per nine innings
HR/9	Average number of home runs given up per nine innings
BB/9	Average number of bases on balls given up per nine innings

(c)At the 0.05 level of significance, test whether the two independent variables added in part (b), the average number of home runs given up per nine innings and the average number of bases on ball given up per nine innings, contribute significantly to the estimated regression equation developed in part

(a).State the null and alternative hypotheses.H₀: ₁ = 0 H_a: ₁ 0H₀: One or more of the parameters is not equal to zero. H_a: ₂ = ₃ = 0 H₀: ₁ 0 H_a: ₁ = 0H₀: ₂ = ₃ = 0 H_a: One or more of the parameters is not equal to zero.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)p-value =

Is the addition of the variables x₂ and x₃ significant?

Do not reject H₀. We conclude that the addition of the variables x₂ and x₃ is not significant.Reject

H₀. We conclude that the addition of the variables x₂ and x₃ is significant.

Do not reject H₀.

We conclude that the addition of the variables x₂ and x₃ is significant.

Reject H₀. We conclude that the addition of the variables x₂ and x₃ is not significant.