Question

Assume that a sample is used to estimate a population mean. Find the 99.5% confidence interval for a sample of size 278 with a mean of 69.2 and a standard deviation of 19.1. Enter your answer as a tri-linear inequality accurate to 3 decimal places.

Confidence Interval: _______ < μ < _______

Answer 1

To find the 99.5% confidence interval, use the formula: Lower limit = sample mean - (critical value) * (standard deviation / square root of sample size), and Upper limit = sample mean + (critical value) * (standard deviation / square root of sample size). The critical value can be found by subtracting 0.5% from 100%, dividing it by 2, and looking it up in a standard normal distribution table. Plug the given values into the formula to calculate the confidence interval.

Step-by-step explanation:

To find the 99.5% confidence interval, we can use the formula:

Lower limit = sample mean - (critical value) * (standard deviation / square root of sample size)
Upper limit = sample mean + (critical value) * (standard deviation / square root of sample size)

First, we need to find the critical value.

Since we want a 99.5% confidence interval, we subtract 0.5% from 100% to get 99.5%. Then, we divide this value by 2 to get 0.25%. Looking up this value in a standard normal distribution table, we find that the critical value is approximately 2.807.

Now, we can substitute the given values into the formula to calculate the confidence interval:

Lower limit = 69.2 - 2.807 * (19.1 / sqrt(278))

Upper limit = 69.2 + 2.807 * (19.1 / sqrt(278))

Calculating these values gives:

Lower limit ≈ 67.921

Upper limit ≈ 70.479

Therefore, the 99.5% confidence interval for the population mean is approximately 67.921 < μ < 70.479.