Answer to Question #346184 in Statistics and Probability for Corbyn

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 $(167.418, 172.582).$