Question

What is the appropriate z critical value for each of the following confidence levels? a. 95% d. 80% b. 90% e. 85%

Answer 1

Answer:

95% confidence level

$Z = 1.96$

80% confidence level

$Z = 1.28$

90% confidence level

$Z = 1.645$

85% confidence level

$Z = 1.44$

Step-by-step explanation:

For a confidence level of x, the critical value of z is the value of z with a pvalue of p given by the following formula:

$p = 1 - \frac{1-x}{2}$

Then we look at the z-table to find Z with a pvalue of p.

a. 95%

Z with a pvalue of

$p = 1 - \frac{1-x}{2} = 1 - \frac{1-0.95}{2} = 0.975$

So $Z = 1.96$

d. 80%

Z with a pvalue of

$p = 1 - \frac{1-x}{2} = 1 - \frac{1-0.8}{2} = 0.9$

So $Z = 1.28$

b. 90%

Z with a pvalue of

$p = 1 - \frac{1-x}{2} = 1 - \frac{1-0.9}{2} = 0.95$

So $Z = 1.645$

e. 85%

Z with a pvalue of

$p = 1 - \frac{1-x}{2} = 1 - \frac{1-0.85}{2} = 0.925$

So $Z = 1.44$