Confidence Interval for pi in Finite Population Case A population of 790 individ

Question

Confidence Interval for pi in Finite Population Case A population of 790 individuals has unknown proportion pi. A simple random sample of 280 is drawn without replacement. The number of successes in the sample is 125. (a)[2] Check if this is the finite population case. (b)[2] Check if the sampling distribution of the sample proportion can be approximately Normal. (c)[3] Construct the 96% Cl for the population proportion pi. State if pi can be 0.50. (d)[3] Construct the 92% Cl for the population proportion pi. State if pi can be 0.45.

Explanation / Answer

as n/N =280/790>0.1 ; this is finite population case

2) from above p=280/790=0.3544

as np>10 and n(1-p)>10 sample proportion can be approximately normal

3)fromabove std error =((p(1-p)/n)*(N-n)/(N-1))1/2 =0.0137

for 96% CI,z=2.0537

hence confidence interval =sample proportion-/+ z*std error =0.3263 ; 0.3825

as above interval does not contain 0.5 as interval value we can not state that pi can be 0.5.

d)for 92% CI,z=2.05371.7507

hence confidence interval =sample proportion-/+ z*std error =0.3305 ; 0.3784

as above interval does not contain 0.45 as interval value we can not state that pi can be 0.45.

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