Answer to Question #326980 in Statistics and Probability for jsjaja

Question

A sample of 60 Grade 9 students' ages was obtained to estimate the mean age of all Grade 9 students.

X = 15.3 years and the population variance is 16.

a. What is the point estimate for u.?

b. Find the 95% confidence interval for u?

c. Find the 99% confidence interval for u?

Answer 1

$a:\\\hat{\mu}=\bar{x}=15.3\\b:\\\left( \bar{x}-\frac{\sigma}{\sqrt{n}}z_{\frac{1+\gamma}{2}},\bar{x}+\frac{\sigma}{\sqrt{n}}z_{\frac{1+\gamma}{2}} \right) =\left( 15.3-\frac{4}{\sqrt{60}}\cdot 1.960,15.3+\frac{4}{\sqrt{60}}\cdot 1.960 \right) =\\=\left( 14.2879,16.3121 \right) \\c:\\\left( \bar{x}-\frac{\sigma}{\sqrt{n}}z_{\frac{1+\gamma}{2}},\bar{x}+\frac{\sigma}{\sqrt{n}}z_{\frac{1+\gamma}{2}} \right) =\left( 15.3-\frac{4}{\sqrt{60}}\cdot 2.576,15.3+\frac{4}{\sqrt{60}}\cdot 2.576 \right) =\\=\left( 13.9698,16.6302 \right)$