Question

1.) The proportion of residents in Phoenix favoring the building of toll roads to complete the freeway system is believed to be p=0.3. If a random sample of 100 individuals shows that 25 favor building toll roads, do we have evidence at the 5% level to claim the true proportion is really lower? Show all work! Step 1: Step 2: Step 3: Step 4: Step 5: P-value: Step 6 Step 7:

Answer 1

Date : Answer ) Given, p= 0.3 A candom sample of 25 favor building 100 individual show toll round. 0.25 P= 25 100 Here we use one sample proportion test step 1 : Nuul Hypothesis Hoi p=po Istep 2 Alternative Hypothesis Hi i p <Po Step 3: Here , we use significance 2=0.05 level of Step 4: Given, Po=0:3 is 0.25 & Sample proportion ļ n=100 Istep 5 : Test statistic: Z= 0.25-0.3 P-Po V Poll-Polln C-3*07)/100 z = -1.091 is p=0.1376 P-value p-value step 6: Rejection Region

using a = 0.05 & critical value for a left -tailed test test is Zc - - 1.64 The εejection ßegion for this left-tailed test is R = {2:2<-164} للحميا Step 7: conclusion since observed a = -1.091 7 Z. =-1-64 hypothesis is not bejected Also P-value - 0'1376 7 X=0'05 we fail to &eject Eeject Ho. we conclude that there is no enough evidence to claim that the true proportion is re lower i.e. the true proportion is not lower.