As a pollster, you called 120 voters to know their positions on a California Sta

Question

As a pollster, you called 120 voters to know their positions on a California State's ballot proposition. Only 80% of the voters had time to answer your calls. Of those who answered you, 56 voters favored the proposition. Explain why this situation should not be considered as finite population case. Check if the sampling distribution of the sample proportion can be approximately Normal. Construct the 90% Cl for the favor proportion n. Sketch the Cl. State if it can be 0.45. Construct the 99% Cl for the favor proportion Ji. Sketch the Cl. State if it can be 0.55.

Explanation / Answer

a)as the popualtion here is california state's ballot which seems much larger then (120*0.8=96 people)

hence we can not consider it as a finite population case.

b)here p=56/96 =0.583

hence np=56 and nq=40 whcih is higher then 10 hence it is approximately normal

3) for std error =(p(1-p)/n)1/2 where p=0.583 and n=96

=0.0503

for 90% CI, z=1.64485

hence confidence interval =mean proportion +/- z*std error =0.5005 ; 0.6661

as 0.45 is outside of given interval, we reject it.

d) for 99% CI; z=2.57583

ehnce confidence interval =mean proportion +/- z*std error =0.4537 ; 0.7129

as 0.55 is inside CI, we can not reject it.,

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