Question

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

Answer 1

1.

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

$$E=z_c\times\dfrac{\sigma}{\sqrt{n}}$$ $$n\ge(\dfrac{z_c\sigma}{E})^2$$

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

$$n=977$$

2.

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

$$E=z_c\times\dfrac{\sigma}{\sqrt{n}}$$ $$n\ge(\dfrac{z_c\sigma}{E})^2$$

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

$$n=246$$

3.

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

$$E=z_c\times\dfrac{\sigma}{\sqrt{n}}$$ $$n\ge(\dfrac{z_c\sigma}{E})^2$$

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

$$n=538$$