Question

for problem 1 the claim is equal or not equal? and do we reject Ho?

and in problem 2 why do I have ir wrong

M227 (Statistics) Test the given hypothesi cw 9.1 9.2) Name: IZ given hypothesis. Assume that the samples are independent and that they have been randomly selected A researcher finds that of 1.000 people who said that they attend a religious service at least 1) once a week, 31 stopped to help a person with car trouble. Of 1,200 people interviewed who had not attended a religious service at least once a month, 22 stopped to help a person with car trouble. At the 0.05 significance level, test the claim that the two proportions are h-1000 n2: 1200 1) claim. X, 31 X722 equal. 2 2) Ho :P, = P2 3) Hi: P.7 P22 tails 5) Z = 1.929 [Start, test, 6)2-prop 2 test, enter] 1.93 6) Meject Ho - CASE 2) 7 of 8,500 people vaccinated against a certain disease later developed the disease. 18 of 10,000 people vaccinated with a placebo later developed the disease. Test the claim that the vaccine is effective in lowering the incidence of the disease. Use a significance level of 0.02. "Claim: P, LP₂ -> CASe 3.org 7-1=6 2) Ho: P;= P2 3) Hi: P, LP2 left tail 216 0.021 3.173 9) Z=-5.96 6) Teject Ho case -> 3 7) Sufficient evident to reject the claim of PILP2

Answer 1

Given that, sample one, x1 =7, n1 = 8500, p1= x1/n1=0.001 sample two, x2 = 18, n2 = 10000, p2= x2/n2=0.002 finding a p^ value for proportion p^=(x1 + x2 ) / (n1+n2) p^=0.001 q^ Value For Proportion= 1-p^=0.999 null, Ho: p1 >= p2 ; alternate, H1: p1 < p2 level of significance, a = 0.02 from standard normal table,left tailed z a/2 =2.054 since our test is left-tailed reject Ho, if zo < -2.054 we use test statistic (z) = (p1-p2)/V(p^q^(1/n1+1/n2)) zo =(0.001-0.002)/sqrt((0.001*0.999(1/8500+1/10000)) zo = -1.802 critical value; the value of lz al at los 0.02% is 2.054 we got [20] =1.802 & za | =2.054 make decision; hence value of zo <za and here we do not reject Ho p-value: left tail - Ha : (p < -1.8017) = 0.03579 hence value of po.02 < 0.03579, here we do not reject Ho null, Ho: p1 >=p2 ; alternate, H1: p1 < p2 test statistic: -1.802 critical value: -2.054 decision: do not reject Ho p-value: 0.03579, vaccine is effective in lowering the incidence of disease