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 equation correctly describes the 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

To find the 90% confidence interval for the population mean (μ), we need to use the t-distribution since the population standard deviation is unknown. The formula for the confidence interval is:

CI = X ± t(α/2,df) * (s/√n)

Where X is the sample mean, t(α/2,df) is the t-value from the t-distribution table with degrees of freedom (df) = n - 1 and α = 1 - confidence level, s is the sample standard deviation and n is the sample size.

Substituting the given values, we get:

CI = 40 ± t(0.05,3) * (4/√4)
CI = 40 ± 2.353 * 2
CI = 40 ± 4.706

So, the correct equation is μ = 40 ± 2.353(2), which is choice C.

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