Question

Describe in detail how you would construct a 95% confidence interval for a set of 30 data points whose mean is 20 and population standard deviation is 3. Be sure to show that you know the formula and how to plug into it.

Also, clearly state the margin of error.

Answer 1

Solution :

Given that,

= 20

= 3

n = 30

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z_/2* ( /n)

= 1.96 * (3 / 30)

= 1.07

Margin of error = 1.07