A sample of 26 elements from a normally distributed population is selected. The sample mean is 10 with a standard deviation of 4. The 95% confidence interval for μ is _____.
A) 6.000 to 14.000
B) 9.846 to 10.154
C) 8.384 to 11.616
D) 8.462 to 11.538

Question

Quizplus · Accepted Answer

The formula for a confidence interval for the population mean is:

CI = x̄ ± z*(σ/√n)

where:
x̄ = sample mean
z = z-score for the desired confidence level (1.96 for 95%)
σ = population standard deviation (unknown, so we use the sample standard deviation, s)
n = sample size

Plugging in the values from the problem, we get:

CI = 10 ± 1.96*(4/√26)
CI = 10 ± 1.96*(0.78)
CI = 10 ± 1.53
CI = (8.47, 11.53)

Therefore, the 95% confidence interval for μ is 8.384 to 11.616, which is option C.

A Sample of 26 Elements from a Normally Distributed Population