We draw a random sample of size 25 from the normal population with variance 2.4. If the sample mean is 12.5, what is a 99% confidence interval for the population mean?
A) [11.2600, 13.7400]
B) [11.3835, 13.6165]
C) [11.7019, 13.2981]
D) [11.7793, 13.2207]

Question

Quizplus · Accepted Answer

We use the formula for a confidence interval for the mean:
CI = X̄ ± z* (σ/√n)
where X̄ is the sample mean, σ is the population standard deviation (which we don't know, but we are given the population variance of 2.4, so we take the square root to get σ = √2.4 = 1.549), n is the sample size (25), and z* is the critical value for a 99% confidence interval, which can be found using a table or calculator to be approximately 2.576.

Plugging in the values, we get:
CI = 12.5 ± 2.576 * (1.549/√25)
CI = 12.5 ± 0.952
CI = [11.548, 13.452]

So the closest answer choice is C, [11.7019, 13.2981], which is also in the correct format for a confidence interval.

We Draw a Random Sample of Size 25 from the Normal