Question

In a sample of 50 Belgian employees, the mean gross monthly wage is 2400 euro. The standard deviation in the population is known to be ??=1000 euro.

Find the 80% confidence interval for ??.

Find the 95% confidence interval for ??.

Find the 95% confidence interval for ?? if the sample size in this example 500 instead of 50.

What sample size would you need to limit the margin of error to 50 euro with 95% confidence?

Answer 1

a) At 80% confidence interval the critical value is z_0.1 = 1.28

The 80% confidence interval for is

+/- z_0.1 *

= 2400 +/- 1.28 * 1000/

= 2400 +/- 181.019

= 2218.981, 2581.019

b) At 95% confidence interval the critical value is z_0.025 = 1.96

The 95% confidence interval for is

+/- z_0.025 *

= 2400 +/- 1.96 * 1000/

= 2400 +/- 277.186

= 2122.814, 2677.186

c) For n = 500

The 95% confidence interval for is

+/- z_0.025 *

= 2400 +/- 1.96 * 1000/

= 2400 +/- 87.654

= 2312.346, 2487.654

d) Margin of error = 50

or, z_0.025 * = 50

or, 1.96 * 1000/ = 50

or, n = (1.96 * 1000/50)^2

or, n = 1537