When faced with a power hitter, many baseball teams utilize a defensive shift. A shift usually involves putting three infielders on one side of second base against pull hitters. Many believe that a power hitter’s batting average is lower when he faces a shift defense as compared to when he faces a standard defense. Consider the following batting averages of 10 power hitters over the 2010 and 2011 seasons when they faced a shift defense versus when they faced a standard defense. The data set, labeled Shift, can also be found on the text website.

a. Specify the competing hypotheses to determine whether the use of the defensive shift lowers a power hitter’s batting average.
b. What are the value of the test statistic and the p-value?
c. At the 5% significance level, is the defensive shift effective in lowering a power hitter’s battingaverage?

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Average When Shift 0.239 0.189 0.150 0.186 Average When No Shift 0.270 0.230 0.263 0.251 0.317 0.250 0.232 0.191 0.182 0.205 Player Jack Cust Adam Dunn Prince Fielder Adrian Gonzalez Rvan Howard Brian McCann David Ortiz Carlos Pena Mark Teixeira Jim Thome 0.321 0.245 0.243 0.168 0.211