We draw a random sample of size 25 from the normal population with the 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

Since the sample size is greater than 30, we can use the z-distribution. The critical z-value for a 99% confidence interval can be found using a z-table, and it is equal to 2.576. The formula for the confidence interval is:

CI = sample mean ± (critical value) x (standard error)

where the standard error is equal to the standard deviation of the population divided by the square root of the sample size:

SE = sqrt(variance/sample size) = sqrt(2.4/25) = 0.4899

Plugging in the values, we get:

CI = 12.5 ± (2.576) x (0.4899) = [11.7019, 13.2981]

Thus, the best choice is C, which matches this interval.

We Draw a Random Sample of Size 25 from the Normal