Answer: [tex](17.96,20.64)[/tex]
Step-by-step explanation:
The confidence interval for population mean is given by :-
[tex]\overline{x}\ \pm\ t_{n-1,\alpha/2}\dfrac{s}{\sqrt{n}}[/tex]
Given : [tex]\overline{x}=19.3[/tex]
[tex]s= 3.1[/tex]
n=23, which is a small sample(n<30), so we use t-test.
Significance level: [tex]1-0.95=0.05[/tex]
Critical value : [tex]t_{n-1,\alpha/2}=t_{22,0.025}=2.074[/tex]
Then , the confidence interval for population mean will be :-
[tex]19.3\ \pm\ (2.074)\dfrac{3.1}{\sqrt{23}}\\\\\approx19.3\pm1.34\\\\=(19.3-1.34,19.3+1.34)\\\\=(17.96,20.64)[/tex]
Hence, the 95% confidence interval for the population mean is [tex](17.96,20.64)[/tex]
