Answer: [tex](8.149,\ 13.691)[/tex]
Step-by-step explanation:
Given : Sample size : n= 49, it means its a large sample.
Significance level : [tex]\alpha: 1-0.99=0.01[/tex]
Critical value : [tex]z_{\alpha/2}=2.576[/tex]
Sample mean: [tex]\overline{x}=10.92[/tex]
Standard deviation: [tex]\sigma=7.53[/tex]
The confidence interval for population mean is given by :-
[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=10.92\pm (2.576)\dfrac{7.53}{\sqrt{49}}\\\\\approx10.92\pm2.771=(10.92-2.771,10.92+2.771)=(8.149,\ 13.691)[/tex]
Hence, the 99% confidence interval for population mean= [tex](8.149,\ 13.691)[/tex]