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:  $(3.146,\ 3.454)$

Step-by-step 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 :-

$\overline{x}\ \pm t_{n-1,\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

$=3.30\pm(1.711)\dfrac{0.45}{\sqrt{25}}\\\\\approx3.30\pm0.1540\\\\=(3.30-0.1540,\ 3.30+0.1540)=(3.146,\ 3.454)$

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