Answer to Question #350340 in Statistics and Probability for Jhovan

Question #350340

Given



1. E = 0.03, 0 =



o = 0.57,



90% confidence



2. E = 0.15, o = 1.2,



95% confidence



3. E = 0.05, o = 0.45,



99% confidence



n=



n=



n=



Solution and Answer

1
Expert's answer
2022-06-14T00:02:12-0400

1.

A 90% confidence interval has a z-score (a critical value) zc=1.6449.z_c=1.6449.

E=zc×σnE=z_c\times\dfrac{\sigma}{\sqrt{n}}n(zcσE)2n\ge(\dfrac{z_c\sigma}{E})^2

n(1.6449(0.57)0.03)2n\ge(\dfrac{1.6449(0.57)}{0.03})^2


n=977n=977



2.

A 95% confidence interval has a z-score (a critical value) zc=1.96.z_c=1.96.

E=zc×σnE=z_c\times\dfrac{\sigma}{\sqrt{n}}n(zcσE)2n\ge(\dfrac{z_c\sigma}{E})^2

n(1.96(1.2)0.15)2n\ge(\dfrac{1.96(1.2)}{0.15})^2




n=246n=246


3.

A 99% confidence interval has a z-score (a critical value) zc=2.5758.z_c=2.5758.

E=zc×σnE=z_c\times\dfrac{\sigma}{\sqrt{n}}n(zcσE)2n\ge(\dfrac{z_c\sigma}{E})^2

n(2.5758(0.45)0.05)2n\ge(\dfrac{2.5758(0.45)}{0.05})^2




n=538n=538

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