Question

parts A-D please and thx

The data for a random sample of 8 paired observations are shown in the table to the right. a. What are the appropriate null and alternative hypotheses to test whether the mean for population 2 is larger than that for population 1? b. Conduct the test identified in part a using a= 0.05. c. Find a 95% confidence interval for Interpret this result. d. What assumptions are necessary to ensure the validity of this analysis? Pa

Answer 1

fair Population 1 Population 2 Difference Cd) Со 62 -2 30. 35 2 35 نا 41 4 5 -5 -6 -7 -7 -6 -4 -6 42 60 37 39 42 35 53 31 35 36 6 it 8 Ed=-43 Mean(d) - Ed --43 = -5.375 n Standard deviation (s) = (4-2)² = 1.685 EWS 2 is not a) Hull hypothesis The mean of population larger than that of population 1 Ho: Mozo Alternative hypothesis The mean of population 2 is larger than that of population 1. Hi Mo <o 18 -5.375 -9.022 b.) Test statistic (to) - slun 1-685756 Reflection (riteria Reject to if to <-tagni Reject to if -9.022 < -1.895 =-1.895 Source (image attached)) STATKEY [tagne -tous, ]

satisfied, we Conclusion - As the above condition Reject the Null hypothesis at 15.) level of sigurficance and conclude that mean 2 is larger than of population 1 C.) 95.7. C. I of population mean for ud. talagni sin & < up < d t talkonto [taban-e? to 023,7 = 2.365 Source - STATKEY Cimage attached) -5.375 2.365 × 1.685 -5.375 + 2-365 x 1-685 8 Js = -6.7845 Hp - 3.966 Intes psuetation - We are 951. confident that the true difference mean for the populations will lie in the interval [-6.7849 -3-966] in d. Assumptions necessary * The data is normally distributed (forms bell shaped curve) variable other * The dependent, must be continu ous - * The paired observations are observations are independent of pairs of observations, The data set should not contain outliere . * SOPODOOSTOOMOVE

Statkey Theoretical Distribution T Distribution- Reset Plot T Distribution Left Tail Two-Tail Right Tail 0.40 df 0.35 Edit Parameters 0.30 0.25 0.20 0.050 0.15 0.10 0.05 0.00 -4 -3 -1 0 1 -1.895 Activate Windows

StatKey Theoretical Distribution T Distribution- Reset Plot T Distribution Left Tail Two-Tail Right Tail 0.40 df 7 0.35 Edit Parameters 0.30 0.25 0.20 0.025 0.950 0.025 0.15 0.10 0.05 0.00 -4 -3 -1 0 1 -2.365 2.365 Activate Windows

The test statistic is calculated using the formula mentioned. The critical value is obtained from STATKEY (image attached for reference). We compare the test statistic with critical value and make the required conclusion. The 95% C.I is constructed as shown.