Question

In a study of the length of time that students require to earn bachelor’s degrees, 60 students are randomly selected and they are found to have a sample mean of 4.8 years and a sample standard deviation of 2.2 years, construct a 95% confidence interval estimate of the population mean.

Answer 1

Answer:    $(4.24,\ 5.36 )$

Step-by-step explanation:

The  confidence interval to estimate the population mean is given by :_

$\overline{x}\ \pm\ z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

Given : Sample size : n= 60 , the sample is a large sample (n>30), so we can apply z-test.

Sample mean = $\overline{x}=4.8$

Standard deviation : $\sigma=2.2$

Level of confidence:$1-\alpha=0.95$

$\Rightarrow\ \alpha=0.05$

Then, critical z-value =$z_{\alpha/2}=1.96$

Then, a 95% confidence interval estimate of the population mean will be

$=4.8\ \pm\ (1.96)\dfrac{2.2}{\sqrt{60}}\\\\=4.8\pm0.56=(4.8-11.76, 4.8+11.76)=(4.24,\ 5.36 )$

Hence, the  95% confidence interval to estimate the population mean = $(4.24,\ 5.36 )$.