Answer to Question #187408 in Statistics and Probability for Aerielle Fajardo

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,

What is the point estimate of the population parameter?

Find the 95% confidence interval for the population parameter?

Find the 99% confidence interval for the population parameter?

= 82.5; s = 3. The parent population is normally distributed. Use the 95% confidence level to find the interval estimate for µ.

Answer 1

$n = 11 \\ \bar{x} = 17.3 \\ \sigma^2 = 18 \\ \sigma = 4.24$

The point estimate of the population parameter

$\mu = 17.3 \\ α = 1 -0.95 = 0.05 \\ α/2 = 0.025 \\ Z_{0.025} = ±1.96$

Confidence interval for the population parameter:

$\mu ± Z_{0.025} \times \frac{4.24}{\sqrt{11}} \\ 17.3 ± 1.96 \times 1.278 \\ 17.3 ± 2.50$

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

$α = 1 -0.99 = 0.01 \\ α/2 = 0.005 \\ Z_{0.005} = ±2.58$

Confidence interval for the population parameter:

$\mu ± Z_{0.005} \times \frac{4.24}{\sqrt{11}} \\ 17.3 ± 2.58 \times 1.278 \\ 17.3 ± 3.29$

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