A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. The standard deviation of the amount in each can is 0.14 ounce. The machine is overhauled with new components, and ten cans are filled to determine whether the standard deviation has changed. Assume the fill amounts to be a random sample from a normal population.
$\begin{array}{lllll}
\hline 12.12 & 11.85 & 12.29 & 12.08 & 12.05 \
11.91 & 11.44 & 11.67 & 11.51 & 11.91 \
\hline
\end{array}$
Perform a hypothesis test to determine whether the standard deviation differs from $0.14 \mathrm { o }$ Use the $\alpha = 0.05$ level of significance.
A) Do not reject $H _ { 0 }$.
B) Reject $H _ { 0 }$.

Question

Quizplus · Accepted Answer

The sample standard deviation is calculated and compared to the hypothesized standard deviation using a chi-square test. The calculated chi-square statistic is greater than the critical value at $\alpha = 0.05$, leading to the rejection of $H_0$.

A Machine That Fills Beverage Cans Is Supposed to Put 12.1211.8512.2912.0812.0511.9111.4411.6711.5111.91\begin{array}{lllll}\hline 12.12 & 11.85 & 12.29 & 12.08 & 12.05 \\11.91 & 11.44 & 11.67 & 11.51 & 11.91 \\\hline\end{array}12.1211.91​11.8511.44​12.2911.67​12.0811.51​12.0511.91​​

A Machine That Fills Beverage Cans Is Supposed to Put $\begin{array}{lllll}\hline 12.12 & 11.85 & 12.29 & 12.08 & 12.05 \\11.91 & 11.44 & 11.67 & 11.51 & 11.91 \\\hline\end{array}$