Question

A random sample of size n=25 from N(μ, σ²=6.25) yielded x=60. Construct the following confidence intervals for μ. Round all your answers to 2 decimal places.

a. 95% confidence interval:

95% confidence interval = 60 ± ?

b. 90% confidence interval:

90% confidence interval = 60 ± ?

c. 80% confidence interval:

80% confidence interval = 60 ± ?

Answer 1

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

The 95% confidence interval is

+/- z_0.025 *

= 60 +/- 1.96 * 2.5/

= 60 +/- 0.98

= 59.02, 60.98

b) At 90% confidence interval the critical value is z_0.05 = 1.645

The 90% confidence interval is

+/- z_0.05 *

= 60 +/- 1.645 * 2.5/

= 60 +/- 0.82

= 59.18, 60.82

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

The 80% confidence interval is

+/- z_0.1 *

= 60 +/- 1.28 * 2.5/

= 60 +/- 0.64

= 59.36, 60.64