'-:--" -- ~ -------------- --.-.-------~~~--~~,~~,-~.,~-~-..-~~.--, --~,-~~~-~------~--~,~-opener, we described a study in which patients were assigned to receive either a new treatment: or a standard treatmell! for ~~-revention of heart failure. A total of 1820 patients participated, with 1089 receiving the new treatment and 731 receiving the $~d treatment. The assignment was not made by simple random sampling; instead, an algorithm was used that was designed to U~chaprer 452 Chapter 9 Inferences on Two Samples produce balance between the groups. The following table presents summary statistics describing several health characteristics of rb.= people in each group. :~~3~rr!!f~Elf~_1 , Age ; 64' 11 j 65! 11 - i'SYst~iic p;~~~;-"lir-. ~ -'~-i8---'----r'-~124-'-T"-~ "If- ~., blood .T :- -DiM"t~li~-bloodressur-e-'-i-'--7'i'--T~--iO-~~; p .. '-'72---1"""-"--10--'- - ~ ~~--~------~----""'~~'------""---'---'--" ---.... -.-- -----~-~------. -------. ........ ..:...-.-.- .. .-...... Lc~;;";,,~=;~=fl~~;~~~ ; Treatment for hypertension 63.2 i 63.7 30,6 ' ~ 30.2 L-~~fib~tic>~~~::=~'-:=~---~.,,, l~6 ,=-~l---=....2!:1" 1 Diabetes r-Cigarette s~;~kmg-'-"----- ; .:-. -- --~12.8 --- -l-----,--lU----< ~ - r---"--'---=---'---~-----"':-~""'-~-'-------'.~--~-'--"'-----~-'"--~-""-'--~";;-'~"""""'''-''''''''''""--. i Coronary bypass surgery --**-----~~~~ -.-- ~ ~~. 28.5 -~-"'<-.~- ; -.-~-~-.;' 29.1 ---'---*-*'~""--"""'----.--'----'~-'---< 1 L For each health characteristic, perform a test of the null hypothesis that the group means or group proportions are equal versus !:be - alternative that they are not equal. State the P -value for each test. 2. Based on the P -values computed in Exercise 1. for which health Ifharacteristics does it appear that the assignment to groups is lXE balanced? Use the 0.05 level of significance. . 3. For each health characteristic, construct a 95% confidence interval for the difference between the group means or group proportioas, 4. Based on the confidence intervals in Exercise 3, for which health characteristics does it appear that the assignment to groups is not balanced? 5. Are the answers to Exercises 2 and 4 the same? Explain. 6. Based on the confidence intervals in Exercise 3, does it appearthat the imbalance is large enough to be of concern: Explain