Please solve the first question using r studio and the second one is short answers(written).

(30 pts) A number of sedentary individuals were selected to participate in a study designed to test the effects of endurance training on resting heart rate. 30 individuals underwent an endurance training regimen for six weeks, while 30 other individuals acted as a control group, maintaining their current activity level. The hr.csv" data set records the resting heart rate values for those keeping their current activity level (sedentary) and for those doing the regimen for six weeks (endurance). The experiment attempts to determine whether subjects who complete the six-week training regimen observe any significant change in heart rate compared to those who didn't do the training (a) What type of test would be appropriate for this data set, and why? (b) Read the hr.csv" file in RStudio and construct an appropriate plot for the vari- able(s) in question. No further explanations are needed here, just the plot(s). (c) Obtain an appropriate 95% two-sided confidence interval for the test statistic. (d) Perform an appropriate hypothesis test at confidence level a = 0.05. List both the t-statistic and its resulting p-value. (e) Do you reject or fail to reject the null hypothesis? (f) What can you conclude about the effect of the training regimen on resting heart rate (assuming the absence of outside factors, and based on your answer in the previous question)? (g) Give an example of a potential confounding variable that could exist for this data set (what is another factor that could influence resting heart rate?). (15 pts.) Answer the following short questions related to samples and sampling distri- butions: (a) If a given sample has a much higher median than mean, would it be left-skewed or right-skewed? Justify your answer with the properties of the mean. (b) If you compare a 95% confidence interval and a 99% confidence interval for the same data, which one will be wider? Justify your answer with the properties of the confidence interval's structure. (c) If a 99% confidence interval from the t-distribution and a 99% confidence interval from the Normal distribution with identical sample error are compared, which one will be wider? Justify your answer with the properties of the t-distribution in relation to the normal distribution (you may want to refer to qt() and qnorm()). a a (30 pts) A number of sedentary individuals were selected to participate in a study designed to test the effects of endurance training on resting heart rate. 30 individuals underwent an endurance training regimen for six weeks, while 30 other individuals acted as a control group, maintaining their current activity level. The hr.csv" data set records the resting heart rate values for those keeping their current activity level (sedentary) and for those doing the regimen for six weeks (endurance). The experiment attempts to determine whether subjects who complete the six-week training regimen observe any significant change in heart rate compared to those who didn't do the training (a) What type of test would be appropriate for this data set, and why? (b) Read the hr.csv" file in RStudio and construct an appropriate plot for the vari- able(s) in question. No further explanations are needed here, just the plot(s). (c) Obtain an appropriate 95% two-sided confidence interval for the test statistic. (d) Perform an appropriate hypothesis test at confidence level a = 0.05. List both the t-statistic and its resulting p-value. (e) Do you reject or fail to reject the null hypothesis? (f) What can you conclude about the effect of the training regimen on resting heart rate (assuming the absence of outside factors, and based on your answer in the previous question)? (g) Give an example of a potential confounding variable that could exist for this data set (what is another factor that could influence resting heart rate?). (15 pts.) Answer the following short questions related to samples and sampling distri- butions: (a) If a given sample has a much higher median than mean, would it be left-skewed or right-skewed? Justify your answer with the properties of the mean. (b) If you compare a 95% confidence interval and a 99% confidence interval for the same data, which one will be wider? Justify your answer with the properties of the confidence interval's structure. (c) If a 99% confidence interval from the t-distribution and a 99% confidence interval from the Normal distribution with identical sample error are compared, which one will be wider? Justify your answer with the properties of the t-distribution in relation to the normal distribution (you may want to refer to qt() and qnorm()). a a