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Answer:
a) the sample size is 400
b) 95% confidence Interval for p is ( 0.0286, 0.0714 )
Step-by-step explanation:
Given the data in the question;
sample size n = 400
x = 20
p = x / n = 20 / 400 = 0.05
q = 1 - p = 1 - 0.05 = 0.95
a)
n = 400
Hence, the sample size is 400
b) 95% confidence Interval for p;
At 95% confidence interval,
significance level ∝ = 1 - 95% = 1 - 0.95 = 0.05
∝/2 = 0.05 / 2 = 0.025
so, Z critical Value ; = 1.96 { from table }
So for Confidence Interval for p;
⇒ p' ± √( p'q' / n )
we substitute
⇒ 0.05 ± 1.96√( (0.05 × 0.95 ) / 400 )
⇒ 0.05 ± 1.96√( 0.00011875 )
⇒ 0.05 ± 1.96 × 0.010897
⇒ 0.05 ± 0.021358
⇒ ( 0.05 - 0.021358 ), ( 0.05 + 0.021358 )
⇒ ( 0.0286, 0.0714 )
Therefore, 95% confidence Interval for p is ( 0.0286, 0.0714 )