Answer)
A)
P = 0.73
N = sample size = 400
Value of the proportion = n*p = 400*0.73 = 292
B)
Standard error = √p*(1-p)/√n
= √{0.73*(1-0.73)}/√400
Standard error = 0.0221979728804
C)
First we need to check the conditions of normality
That is if n*p and n*(1-p) both are greater than 5 or not
N*p = 292 > 5
N*(1-p) = 108 > 5
As both the conditions are met, we can use standard normal z table to estimate the interval
From z table, critical value z for 95% confidence level is 1.96.
Margin of error = z*standard error = 1.96*0.0221979728804
MOE = 0.0435080268456
Confidence interval is given by,
(P-MOE, P+MOE)
(0.6864919731543, 0.7735080268456)
D)
We are 95% confident that true population proportion lies in the interval (0.686, 0.774)
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