Question

Soccer demands a high fitness level. In 2015-2016, cSUMB Women's Soccer Team collected data on YBMI test. The YBMI test, which stands for You Better Make It, consists of six phases . Run 800 meters (2-minute rest) Run 400 meters (2-minute rest) Shuttte Sprin (1-minute rest) Shuttte Sprint (1-minute rest) Run 400 meters (2-minute rest) Run 800 meters (done) The passing time is 9 minutes excluding the rest times. The team training started in November 2015 to prepare their season starting in April 2016. To monitor players' itness, the first data collection happened at the end of November (pre), and the second data collection happened at the end of February (post). The coach needed evidence to confirm that players improved their fitness level. Let uD denote the average difference of YBMI test result (in seconds) when the post is compared to the pre. Dowaload YBMI csv Note that the data are not ready to be analyzed. Use the following R code to obtain paired diferences (D....D) named diff in the code R Code data r๑ad . csv ( file , choose () ) head (data) data pre subset data, testpre") data postsubsetdata, test"post head (data pre) head (data post) xdata prestine ydata poststine diff Assume (D,... , Du) is a sample from a normal distribution. a. State Ho and H , in terms of μD. (Recall the interpretation of μ D, and think carefully if it should be a left-tail or right-tail test.) b. State the decision rule. c. Caleulate the T statistie and p-value d. Is Ho rejected in favor of H? e. State the conclusion in the context of the problem. (Try not to use the symbols Ho, Hi, and μ) f. By how many seconds did the players improve on average? id es time 1 pre 607 1 post 554 pre 520 2 post 509 3 pre 598 3 post 510 4 pre 559 4 post S51 5 pre 644 5 post 513 6 pre 620 6 post 546 7 pre 530 7 post 498 8 pre 544 8 post 503 9 pre 597 9 post 473 10 pre 594 10 post 532 11 pre 623 11 pos 501 12 pre 557 12 post 542 13 pre 607 13 post 496 14 pre 621 14 post 478 15 pre 528 15 post 516 16 pre 660 16 post 531

Answer 1

R code and explanation given below

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rawdata <-read . csv ( " rawdata.csv", header T, stringsAs Factors F) = pre <- subset (rawdata, rawdataStest-"pre") post <- subset (rawdata, rawdataStest "post") x-preStime pos t $time t.test (x, y, paired T, alternative- "less") = ## Paired t-test ## data: x and y ## t 5.8632, df 15, p-value- 1 # alternative hypothesis: true difference in means is less than 0 ## 95 percent confidence interval: -Inf 93.85209 ## sample estimates: ## mean of the differences 72.25 Hypothesis This corresponds to a left tailed test Rejection rule For the a-0.05 and df-15, we find the critical value critical-1.753 We reject the null hypothesis if the tstat less than tcritical

Test statistics tstat 5.863 Descision Since the tstat is greater than tcritical we fail to reject the null hypothesis. We conclude that the avearge time to complete the YBMI test is lesser after the training. On an average the players improved by 72.25 seconds