2. The athletics department wanted to examine heart rates of athletes before and after a new exercise. The athletics dep

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2 The Athletics Department Wanted To Examine Heart Rates Of Athletes Before And After A New Exercise The Athletics Dep 1 (330.44 KiB) Viewed 24 times

2. The athletics department wanted to examine heart rates of athletes before and after a new exercise. The athletics department recruited a random sample of 27 Rutgers athletes. Department staff measured each athlete's heart rate before the athlete started the exercise program and after the athlete completed the exercise program. The staff compared the average heart rate before and after the exercise program using type l error of 0.05. Two computer outputs of their analysis using the R programming language are given below. Choose the correct analysis output and answer the questions given below. > t.test(heart. rate. before. exercise, heart.rate. after.exercise, paired=F) Welch Two Sample t-test data: heart. rate. before. exercise and heart. rate. after.exercise t = 1.3212, df = 50.611, p-value = 0.1924 alternative hypothesis: true difference in means is not equal to O 95 percent confidence interval: -3.272751 15.865344 sample estimates: mean of x mean of y 105.48148 99.18519 > t.test(heart. rate. before. exercise, heart. rate. after.exercise, paired=T) Paired t-test data: heart. rate. before. exercise and heart. rate. after.exercise t = 2.455, df = 26, p-value = 0.02109 alternative hypothesis: true difference in means is not equal to o 95 percent confidence interval: 1.024426 11.568166 sample estimates: mean of the differences 6.296296 a. Write your null and alternative hypotheses. [0.2 point] b. Give the value of the test statistic from the output. [0.2 point] c. What is the sampling distribution of the test statistic? [0.2 point] d. Give the degrees of freedom for the sampling distribution of your test statistic from the output. [0.2 point. do not just give the formula for degrees of freedom or say how the degrees of freedom might be calculated - give the actual number of the degrees of freedom from the output. If you only give the formula or the method for calculating the degrees of freedom without giving the actual number, you will get 0 points.] e. Write your scientific conclusion by including the p-value in parentheses. [Avoid saying "fail to reject” or “reject” the null hypothesis in your scientific statement]. [0.2 points]