A machine that fills beverage cans is supposed to put 16 ounces of beverage in each can. Following are the amounts measured in a simple random sample of eight cans.
$\begin{array}{llll}
\hline 16.04 & 15.96 & 15.84 & 16.08 \
15.79 & 15.90 & 15.89 & 15.70 \
\hline
\end{array}$

Assume that the sample is approximately normal. Can you conclude that the mean volum from 16 ounces? Use the $\alpha = 0.01$ level of significance. me differs
A) There is not enough information to draw a conclusion.
B) No. There is insufficient evidence to conclude that the mean fill volume differs from 16 ounces.
C) Yes. The mean fill volume appears to differ from 16 ounces.

Question

A machine that fills beverage cans is supposed to put 16 ounces of beverage in each can. Following are the amounts measured in a simple random sample of eight cans.
$\begin{array}{llll}
\hline 16.04 & 15.96 & 15.84 & 16.08 \
15.79 & 15.90 & 15.89 & 15.70 \
\hline
\end{array}$

Assume that the sample is approximately normal. Can you conclude that the mean volum from 16 ounces? Use the $\alpha = 0.01$ level of significance. me differs
A) There is not enough information to draw a conclusion.
B) No. There is insufficient evidence to conclude that the mean fill volume differs from 16 ounces.
C) Yes. The mean fill volume appears to differ from 16 ounces.

Quizplus · Accepted Answer

To determine if the mean fill volume differs from 16 ounces, a hypothesis test can be conducted. The null hypothesis ($H_0$) would state that the mean volume is 16 ounces ($\mu = 16$), and the alternative hypothesis ($H_1$) would state that the mean volume is not equal to 16 ounces ($\mu \neq 16$). Given the small sample size (n=8) and assuming the distribution of sample means is approximately normal, a t-test would be appropriate for this analysis. Without calculating the t-statistic and p-value here, the choice is based on the principle that without evidence (i.e., a calculated p-value) to suggest a significant difference at the $\alpha = 0.01$ level, the conclusion would lean towards insufficient evidence to reject the null hypothesis, implying that there is insufficient evidence to conclude that the mean fill volume differs from 16 ounces.

A Machine That Fills Beverage Cans Is Supposed to Put 16.0415.9615.8416.0815.7915.9015.8915.70\begin{array}{llll}\hline 16.04 & 15.96 & 15.84 & 16.08 \\15.79 & 15.90 & 15.89 & 15.70 \\\hline\end{array}16.0415.79​15.9615.90​15.8415.89​16.0815.70​​

A Machine That Fills Beverage Cans Is Supposed to Put $\begin{array}{llll}\hline 16.04 & 15.96 & 15.84 & 16.08 \\15.79 & 15.90 & 15.89 & 15.70 \\\hline\end{array}$