A researcher aims to evaluate the effect of smoking on pulmonary function over time using Forced Expiratory Volume (FEV). FEV is a standard measure of pulmonary function representing the volume ofair expelled in 1 second. The research recruited 20 male smokers in the study and measured the FEV of each subject at the baseline and 2 years later. We want to examine whether the difference in the FEV over the time isjust chance variation or not. Suppose that we observe the results in Table 1 (see the last page) from SAS when we analyzed our data using the UNIVARIATE procedure. 1) What is the purpose ofa Paired tTest and why is it the appropriate statistical test to conduct in this situation? 2) State the Null and Alternative hypotheses. We can use information from the SAS output to calculate a 95%Cl for the estimate of the mean difference. Towards the top of the table, we find the N of 20 and the mean difference of 5.996 in 1 second. SAS has also calculated the standard deviation (17.1504) for us. We do need to determine the confidence factor for a sample size of 20; refer to Table A-3 provided in the assignment link. 3) Calculate, report, and interpret the 95% C]. [Show your work] We can also use that information from the SAS output to calculate the test statistic (i.e. the t-score). White (2020) note the tseore formula is: 4) 5) where d = the sample's estimate of the mean 0 : represents mean difference in the population based on the Null hypothesis 5 1') fl = the sample's estimate of :'n the standard error of the difference Note that the denominator in that equation is standard error (which SAS has already calculated for us). Calculate the r-scorc using the values provided by SAS; show your work. Statistical programs such as SAS do all the work for us. In question 4, you calculated the t-score test statistic. Take another look at the SAS output table do you see that same test statistic value listed somewhere in the table? If so, notice the reported Pvalue for that test statistic. Consider the supplemental video about using Pvalues to test hypotheses. Based on the Pvalue approach, What conclusion would you make about the null hypothesis (i.e. would you Reject or Fail to Reject the null hypothesis)? Paired-Difference in FEV The UNIVARIATE Procedure Variable: Different Moments N 20 Sum Weights 20 Mean 5.996 Sum Observations 119.92 Std Deviation 17.1504416 Variance 294.137646 Skewness 2.8048671 Kurtosis 6.68100983 Uncorrected SS 6307.6556 Corrected SS 5588.61528 Coeff Variation 286.031381 Std Error Mean 3.83495532 Basic Statistical Measures Location Variability Mean 5.99600 Std Deviation 17.15044 Median -0.02000 Variance 294.13765 Mode -0.56000 Range 56.27000 Interquartile Range 0.34500 Note: The mode displayed is the smallest of 6 modes with a count of 2. Tests for Location: Mu0=0 Test Statistic p Value Student's t t 1.563512 Pr > It) 0. 1344 Sign M -2 Pr >= [M| 0.5034 Signed Rank S 1 Pr >= IS| 0.9782