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)`

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)(\sigma)/(√(n))\\\\=59.8\pm(1.645)(9.2)/(√(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)`