Question

A simple random sample of size n = 21 is drawn from a population that is normally distributed. The sample mean is found to be x = 66 and the sample standard deviation is found to be s = 12. Construct a 90% confidence interval abeut the population mean.

Answer 1

To construct a 90% confidence interval about the population mean, use the formula CI = x ± (Z * (s / sqrt(n))) where x is the sample mean, s is the sample standard deviation, n is the sample size, and Z is the z-score corresponding to the desired confidence level. For a 90% confidence level, the z-score is 1.645. Plugging the given values into the formula, we get the confidence interval (62.792, 69.208).

Step-by-step explanation:

To construct a 90% confidence interval about the population mean, we need to use the formula:

CI = x ± (Z * (s / sqrt(n)))

In this formula, x is the sample mean, s is the sample standard deviation, n is the sample size, and Z is the z-score corresponding to the desired confidence level.

For a 90% confidence level, the z-score is 1.645. Plugging the given values into the formula:

CI = 66 ± (1.645 * (12 / sqrt(21)))

Calculating this expression, we get the confidence interval (62.792, 69.208).