Answer to Question #216150 in Statistics and Probability for Henie

Question

A sample of 60 grade 11 students ages was obtained to estimate the mean age of all grade 12 students.x=16..8 years and the population variance is 16

A. What is the point estimate for μ?
B. Find the 95% confidence interval for μ?
C. What conclusion can you make based on each estimate?

Answer 1

$\bar{x}=16.8 \\ \sigma = \sqrt{16}=4 \\ n=60$

A. The point estimate for \mu is the mean age for grade 11 students included in the sample of 60 students. In this case, the mean age of grade 11 students included in the sample is 16.8 years. The point estimate for \mu is 16.8 years.

B. Two-sided confidence interval:

$CI = (\bar{x} - \frac{Z_c \times \sigma}{\sqrt{n}}, \bar{x} + \frac{Z_c \times \sigma}{\sqrt{n}}) \\ CI = (16.8 - \frac{1.96 \times 4}{\sqrt{60}}, 16.8 + \frac{1.96 \times 4}{\sqrt{60}}) \\ CI = (16.8 -1.01, 16.8 + 1.01) \\ CI = (15.79, 17.81)$

C. (15.79, 17.81) is a range of values (upper and lower) that you can be 95% certain contains the true mean of the population.