Answer:
Hence, the mean of the potato chips lie between the interval [tex](1.006, 1.194)[/tex]
Given :
data is :
[tex]1.1,1.2,1.0,0.9,1.1,1.3,1.2,1.1,1.0[/tex]
Confidence level is [tex]95\%[/tex].
To find :
Confidence interval.
Explanation :
Mean [tex]\bar{x}[/tex] [tex]=\frac{\sum x}{n}[/tex]
[tex]\Rightarrow \bar{x}=\frac{1.1+1.2+1.0+0.9+1.1+1.3+1.2+1.1+1.0}{9}[/tex]
[tex]\Rightarrow \bar{x}=\frac{9.9}{9}[/tex]
[tex]\Rightarrow \bar{x}=1.1[/tex]
Standard deviation [tex]\sigma[/tex] [tex]=\sqrt{\frac{\sum (x-\bar{x})^2}{n-1}}[/tex]
[tex]\Rightarrow \sigma=\sqrt{\frac{\sum (x-\bar{x})^2}{n-1}}=0.122[/tex]
here, [tex]\alpha=1-\;\text{confidence level}[/tex]
[tex]\Rightarrow \alpha=1-0.95=0.05[/tex]
[tex]Z_{\frac{\alpha}{2}}=Z_{0.05}=2.306[/tex] by the Z- table
[tex]95\%[/tex] confidence interval is :
[tex]\bar{x}\pm Z_{\frac{\alpha}{2}}\times \frac{\sigma}{\sqrt{n}}[/tex]
[tex]\Rightarrow 1.1\pm 2.306\times \frac{0.122}{\sqrt{9}}[/tex]
[tex]\Rightarrow 1.1\pm 2.306\times \frac{0.122}{3}[/tex]
[tex]\Rightarrow 1.1\pm 0.094[/tex]
[tex]\Rightarrow (1.006, 1.194)[/tex]
Therefore, the mean of the potato chips lie between the interval [tex](1.006, 1.194)[/tex]
