Answer: [tex](323.5,\ 390.5)[/tex]
Step-by-step explanation:
The confidence interval for population mean is given by :-
[tex]\overline{x}\pm t_{n-1,\ \alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]
Given : Sample size : [tex]n=8[/tex] , which is a small sample (n<30) , so we apply t-test .
Sample mean : [tex]\overline{x}=357\text{ nanograms per gram (ng/g)}[/tex]
Standard deviation : [tex]\sigma= 50\text{ nanograms per gram (ng/g)}[/tex]
Significance level : [tex]\alpha=1-0.9=0.1[/tex]
Critical value : [tex]t_{n-1,\alpha/2}=t_{7, 0.05}=1.895[/tex]
Now, a 90% confidence interval to estimate the mean level of pesticide in minke whales in this region will be :-
[tex]357\pm(1.895)\dfrac{50}{\sqrt{8}}\\\\\approx357\pm33.50\\\\=(357-33.50,\ 357+33.50)\\\\=(323.5,\ 390.5)[/tex]
Hence, the 90% confidence interval to estimate the mean level of pesticide in minke whales in this region is [tex](323.5,\ 390.5)[/tex]
