Answer to Question #309909 in Statistics and Probability for Zack

Question

A random sample of size 36 was taken from a population distributed as Nμ,3.92.The value of the sample x was 15.6. i. Find a 90% confidence interval for μ. (5mks)

It is believed that value of μ is 17. Use your confidence interval to comment on this belief.(2mks)

Answer 1

The confidence interval is

$\left( \bar{x}-\frac{\sigma}{\sqrt{n}}z_{\frac{1+\gamma}{2}},\bar{x}+\frac{\sigma}{\sqrt{n}}z_{\frac{1+\gamma}{2}} \right) =\left( 15.6-\frac{3.92}{\sqrt{36}}\cdot 1.65,15.6+\frac{3.92}{\sqrt{36}}\cdot 1.65 \right) =\\=\left( 14.552,16.678 \right)$

Since 17 doesn’t lie within the confidence interval, the belief is false with confidence level 0.9.