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 $0.12$ ounce. The machine is overhaul, with new components, and ten cans are filled to determine whether the standard deviation changed. Assume the fill amounts to be a random sample from a normal population.
$\begin{array}{lllll}
\hline 12.14 & 12.05 & 12.27 & 11.89 & 12.06 \
12.14 & 12.05 & 12.38 & 11.92 & 12.14 \
\hline
\end{array}$

Perform a hypothesis test to determine whether the standard deviation differs from $0.12$ o Use the $\alpha = 0.05$ level of significance.
A) Do not reject $H _ { 0 }$.
B) Reject $H _ { 0 }$. ounce.

Question

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 $0.12$ ounce. The machine is overhaul, with new components, and ten cans are filled to determine whether the standard deviation changed. Assume the fill amounts to be a random sample from a normal population.
$\begin{array}{lllll}
\hline 12.14 & 12.05 & 12.27 & 11.89 & 12.06 \
12.14 & 12.05 & 12.38 & 11.92 & 12.14 \
\hline
\end{array}$

Perform a hypothesis test to determine whether the standard deviation differs from $0.12$ o Use the $\alpha = 0.05$ level of significance.
A) Do not reject $H _ { 0 }$.
B) Reject $H _ { 0 }$. ounce.

Quizplus · Accepted Answer

The hypothesis test for variance (or standard deviation) is a chi-square test. The null hypothesis ($H_0$) states that the population standard deviation is equal to 0.12 ounces. The alternative hypothesis ($H_a$) suggests that the standard deviation is not equal to 0.12 ounces. Given the sample size (n=10) and the sample standard deviation, we calculate the chi-square statistic and compare it to the critical values from the chi-square distribution for $n-1 = 9$ degrees of freedom at the $\alpha = 0.05$ level of significance. Without the exact calculation here, the conclusion to not reject $H_0$ implies that the sample data do not provide sufficient evidence to conclude that the standard deviation of the fill amounts differs from 0.12 ounces after the machine overhaul.

A Machine That Fills Beverage Cans Is Supposed to Put 0.120.120.12

A Machine That Fills Beverage Cans Is Supposed to Put $0.12$