A sample of n = 4 scores is selected from a population with an unknown mean.The sample has a mean of M = 40 and a variance of s² = 16.Which of the following is the correct 90% confidence interval for μ?
A)μ = 40 ± 2.353(4)
B)μ = 40 ± 1.638(4)
C)μ = 40 ± 2.353(2)
D)μ = 40 ± 1.638(2)

Question

Quizplus · Accepted Answer

The formula for a confidence interval with known variance is:

CI = M ± z(α/2) * (σ/√n)

where M is the sample mean, σ is the population standard deviation (unknown in this case), n is the sample size, and z(α/2) is the z-score corresponding to the desired confidence level (in this case, 90%, so z(α/2) = 1.645).

Substituting the given values, we get:

CI = 40 ± 1.645 * (4/√4)
CI = 40 ± 1.645 * 2

Simplifying, we get:

CI = 40 ± 3.29

Therefore, the correct answer is C: μ = 40 ± 2.353(2).

A Sample of N = 4 Scores Is Selected from a Population