Question

Randomly selected students participated in an experiment to test their ability to determine when one minute​ (or sixty​ seconds) has passed. Forty students yielded a sample mean of 59.8 seconds. Assuming that sigmaequals9.2 ​seconds, construct and interpret a 90​% confidence interval estimate of the population mean of all students.

Answer 1

Answer: $(57.41,\ 62.19)$

Step-by-step explanation:

Given : Sample size : $n=40$

Sample mean : $\overline{x}=59.8\text{ seconds}$

Standard deviation : $\sigma =9.2\text{ seconds}$

Significance level : $\alpha=1-0.9=0.1$

Critical value : $z_{\alpha/2}=1.645$

Formula to find the confidence interval for population mean :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=59.8\pm(1.645)\dfrac{9.2}{\sqrt{40}}\\\\\approx59.8\pm2.39\\\\=(59.8-2.39,\ 59.8+2.39)\\\\=(57.41,\ 62.19)$

Hence, a 90​% confidence interval estimate of the population mean of all students = $(57.41,\ 62.19)$