Answer: (40.33, 43.67)
Step-by-step explanation:
Given : Sample size : n= 15<30 , which is a small sample so we use t-test.
Sample mean : [tex]\overline{x}=42[/tex]
Standard deviation : [tex]\sigma=3[/tex]
Significance level : [tex]\alpha: 1-0.95=0.05[/tex]
Critical value : [tex]t_{n-1,alpha/2}=t_{14,0.025}=2.15[/tex]
The confidence interval for population mean is given by :-
[tex]\overline{x}\pm\ t_{n-1,\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=42\pm(2.15)\dfrac{3}{\sqrt{15}}\\\\\approx42\pm1.67\\\\=(40.33,\ 43.67)[/tex]
Hence, the 95% confidence level. interval for the population mean is (40.33, 43.67).
