Given:
40,31,32,16,25,35,22,53,23 and 33.
a)
Sample mean:
[tex]\bar{x}=32[/tex]Population mean:
[tex]\mu=\frac{\Sigma(x_i)}{n}_{}[/tex][tex]\mu=\frac{40+31+32+16+25+35+22+53+23+33}{10}[/tex][tex]\mu=\frac{310}{10}[/tex][tex]\mu=31[/tex]b)
[tex]\sigma=\sqrt[]{\frac{\Sigma(x-\mu)^2}{n-1}}[/tex][tex]\sigma=\sqrt[]{\frac{81+0+1+225+36+16+81+484+64+4}{10-1}}[/tex][tex]\sigma=\sqrt[]{\frac{992}{9}}[/tex][tex]\sigma=\frac{\sqrt[]{992}}{3}[/tex][tex]\sigma=10.4987[/tex][tex]\text{Error}=\pm z\times\frac{\sigma}{\sqrt[]{n}}[/tex]z value is not given so taken as 95% on confidence level
[tex]z=1.96[/tex][tex]\text{Error}=\pm1.96\times\frac{10.4987}{\sqrt[]{10}}[/tex][tex]\text{Error}=\pm6.5072[/tex][tex]\text{Error}=\pm6.5[/tex]