Given a sample mean of 12.5-drawn from a normal population, a sample of size 25, and a sample variance of 2.4-find a 99% confidence interval for the population mean.
A) [11.7019, 13.2981]
B) [11.1574, 13.8426]
C) [11.6334, 13.3666]
D) [11.7279, 13.2721]

Question

Quizplus · Accepted Answer

We use the formula: 
CI = x̄ ± z*(σ/√n)
Where x̄ = sample mean = 12.5, σ² = population variance = 2.4, n = sample size = 25, z = z-score from the standard normal distribution at the 99% confidence level (∝/2 = 0.005, so z = 2.576).

Plugging in the values, we get:
CI = 12.5 ± 2.576*(√2.4/√25) = [11.6334, 13.3666]

Therefore, the best choice is C.

Given a Sample Mean of 12