Confidence Interval for pi in Finite Population Case A population of 790 individ
ID: 3229620 • Letter: C
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.