4. Strikes "' Advertisements for an instructional video claim that the techniques taught in the video will improve the ability of Little League pitchers in baseball to throw strikes. To test this claim, a researcher selected a random sample of 20 Little Leaguers and had each throw 50 pitches both before and after watching the video, recording the number of strikes. The data were summarized using R, with the difference in number of strikes thrown defined as Difference = After Before. Rcmdr> numSummary(Str'i kes [ , c("After", "Before", "D'i fference")], Rcmdr+ statfstfcs=c("mean","sd","IQR","quant'i'|es"), quant'i'les=c(0, .25,.5,.75.1)) mean sd IQR 0% 25% 50% 75% 100% n After 33.15 2.323224 3.00 28 32 33.0 35.00 37 20 Before 33.05 2.438183 2.25 28 32 33.0 34.25 37 20 Difference 0.10 3.322966 4.00 -5 -2 -0.5 2.00 7 20 95 percent confidence 'interval: -1.455196 1.655196 samp'le est'imates: mean of the differences 0.1 The researcher would like to assess if the number of strikes thrown after watching the video was significantly higher on average, namely, Ho: ud = 0 versus Ha: pd > 0. a. Provide the test statistic value used to test the hypotheses stated above. Show all work. [2] 0.10 0 t = 3.322966 /J2_0 b. Report the (bounds for the) p-value for the hypotheses stated above. [2] The p-value is the area to the right of 0.1346 under a t distribution with 19 df. Using Table A.3 we have pvalue > 0.108. mm Using a calculator with a built in t distribution would give an actual pvalue of 0.4472 (but need to have some information or sketch about what you are nding if the calculator was used). = 0.1602 Final answer: 0.1602 hours