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 )`

Explanation:

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

`\overline{x}\ \pm\ z_(\alpha/2)(\sigma)/(√(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)(2.2)/(√(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 )`.