Answer to Question #332493 in Statistics and Probability for Ralfh

Question

A Random sample of 60 grade 11 students ages is obtained to estimate the mean ages of all grade 11 students. Suppose the sample mean is 17.3 and the population variance is 18,

1. What is the point of estimate of the population parameter?

2.Find the 95% confidence interval for the population parameter?

3.Find the 99% confidence interval for the population parameter?

Answer 1

The point estimate of the population parameter

$\mu=17.3$

$\alpha=1-0.95=0.05$

$\alpha/2=0.025$

$Z_{0.025}= \plusmn 1.96$

Confidence interval for the population parameter:

$CI=\mu \plusmn Z\frac{\sigma}{\sqrt{n}}=17.3 \plusmn 1.96\frac{4.24}{\sqrt{11}}=17.3 \plusmn 2.5$

The 95% confidence interval for the population parameter: (14.8, 19.8)

$\alpha=1-0.99=0.01$

$\alpha/2=0.005$

$Z_{0.005}= \plusmn 2.58$

Confidence interval for the population parameter:

$CI=\mu \plusmn Z\frac{\sigma}{\sqrt{n}}=17.3 \plusmn 2.58 \frac{4.24}{\sqrt{11}}=17.3 \plusmn 3.29$

The 95% confidence interval for the population parameter: (14.01, 20.59)