Question

A random sample of 64 observations has a mean of 30. The population variance is assumed to be 9. The 85.3% confidence interval estimate for the population mean (to the third decimal place) is:

A) (29.206, 30.794)
B) (28.401, 31.599)
C) (28.992, 31.008)
D) (29.832, 30.168)

Answer 1

The 85.3% confidence interval estimate for the population mean is (29.206, 30.794).

Step-by-step explanation:

To find the confidence interval estimate for the population mean, we can use the formula:

CI = Sample Mean ± (Z-value * (Population Standard Deviation / √Sample Size))

Since the sample size is 64, the Z-value for an 85.3% confidence level is approximately 1.062. The population standard deviation is 3, so the confidence interval is:

(30 - (1.062 * (3 / √64)), 30 + (1.062 * (3 / √64)))

Simplifying the expression gives us:

(29.206, 30.794)