A Machine Fills 12 -Ounce Bottles with Soda $0.02$ Ounce a Sample of 8 Bottles Is Selected, and the Machine

Multiple Choice

A machine fills 12 -ounce bottles with soda. For the machine to function properly, the standard deviation of the sample must be less than or equal to $0.02$ ounce. A sample of 8 bottles is selected, and the number of ounces of soda in each bottle is given. At $\alpha = 0.05$ , can you reject the claim that the machine is functioning properly? Justify your answer. (A that the variables are approximately normally distributed.)
$$\begin{array} { l l l l } 12.04 & 11.91 & 11.91 & 11.91 \\11.91 & 11.97 & 12.01 & 12.06\end{array}$$

A) $\chi ^ { 2 } = 72.000 , \chi _ { \text {critical } } ^ { 2 } = 14.067$ ; There is evidence to reject the claim that the machine is working properly.
B) $\chi ^ { 2 } = 65.570 , \chi _ { \text {critical } } ^ { 2 } = 15.507$ ; There is not enough evidence to reject the claim that the machine is working properly.
C) $\chi ^ { 2 } = 72.000 , \chi _ { \text {critical } } ^ { 2 } = 15.507$ ; There is evidence to reject the claim that the machine is working properly.

D) $\chi ^ { 2 } = 65.570 , \chi _ { \text {critical } } ^ { 2 } = 14.067$ ; There is evidence to reject the claim that the machine is working properly.