Question

Mrs oli plans to select 360 grade eleven students obtained from the population. The selected respondents has an average height of 170 cm and a sample standard deviation of 25 cm. What is the 95% confidence interval of all the student's heights?

Answer 1

The critical value for $\alpha = 0.05$ is $z_c = z_{1-\alpha/2} = 1.96.$

The corresponding confidence interval is computed as shown below:

$$CI=(\bar{x}-z_c\times\dfrac{\sigma}{\sqrt{n}},\bar{x}+z_c\times\dfrac{\sigma}{\sqrt{n}})$$

$$=(170-1.96\times\dfrac{25}{\sqrt{360}},170+1.96\times\dfrac{25}{\sqrt{360}})$$

$$=(167.418,172.582)$$

Therefore, based on the data provided, the 95% confidence interval for the population mean is $167.418 < \mu < 172.582,$ which indicates that we are 95% confident that the true population mean $\mu$ is contained by the interval $(167.418, 172.582).$