Question

For a normal population with known variance σ2, answer the following questions:

d. What is the confidence level for the interval μ ≤ x+ 2.00σ∕ √ n?

e. What is the confidence level for the interval x−1.96σ∕ √ n ≤ μ?

Answer 1

Solution:

d)

Given a one sided upper confidence interval for mean

μ ≤ x+ 2.00σ∕ √ n

Formula :   

Comparing , = 2.00

Use z table. See the column of z . See 2.0 and then see the corresponding value at .00

So ,

1 - = 0.9772

= 0.0228

Confidence level c = 1 - = 1 - 0.0228 = 0.9772 = 97.72 % or nearly 98%

Answer : Confidence level is 97.72 % or nearly 98%

e)

Given a one sided lower confidence interval for mean

x−1.96σ∕ √ n ≤ μ?

Formula :   

Comparing , = 1.96

Use z table. See the column of z . See 1.9 and then see the corresponding value at .06

So ,

1 - = 0.975

= 0.025

Confidence level c = 1 - = 1 - 0.025= 0.975= 97.5 %

Answer : Confidence level is 97.5 %