Question

An admissions officer has determined that the population of applicants to the MBA program has undergraduate GPA’s that are approximately normally distributed with standard deviation 0.45. A random sample of 25 applicants for next fall has a sample mean GPA of 3.30. Find the 95% confidence interval for the mean GPA among applicants to this MBA.

Answer 1

Answer:
`(3.146,\ 3.454)`

Explanation:

(a) Given : Sample size :
`n=25`, which is less than 30 so we use t-test.

Sample mean :
`\overline{x}=3.30`

Standard deviation :
`\sigma= 0.45`

Significance level :
`\alpha=1-0.95=0.05`

Critical value :
`t_(n-1,\alpha/2)=t_(24,0.05)=1.711`

The confidence interval for population mean is given by :-

`\overline{x}\ \pm t_(n-1,\alpha/2)(\sigma)/(√(n))`

`=3.30\pm(1.711)(0.45)/(√(25))\\\\\approx3.30\pm0.1540\\\\=(3.30-0.1540,\ 3.30+0.1540)=(3.146,\ 3.454)`

Hence, the 95% confidence interval for the mean GPA among applicants to this MBA =
`(3.146,\ 3.454)`