Two coffee-vending machines are studied to determine whether they distribute the same amounts.Samples are taken and the number of ounces is recorded for each machine. $$\begin{array} { c c }
\text { Machine A } & \text { Machine B } \
\hline 6.10 & 5.99 \
5.95 & 6.01 \
5.98 & 5.98 \
6.01 & 5.96 \
6.00 & 6.08 \
5.95 & 5.89 \
6.02 & 6.01 \
6.04 & 6.00 \
5.99 & 5.97 \
6.06 & 6.00
\end{array}$$
What is the test statistic T?
A)116
B)94
C)131
D)79

Question

Two coffee-vending machines are studied to determine whether they distribute the same amounts.Samples are taken and the number of ounces is recorded for each machine. $$\begin{array} { c c } 
\text { Machine A } & \text { Machine B } \
\hline 6.10 & 5.99 \
5.95 & 6.01 \
5.98 & 5.98 \
6.01 & 5.96 \
6.00 & 6.08 \
5.95 & 5.89 \
6.02 & 6.01 \
6.04 & 6.00 \
5.99 & 5.97 \
6.06 & 6.00
\end{array}$$
What is the test statistic T?
A)116
B)94
C)131
D)79

Quizplus · Accepted Answer

The test statistic T is calculated as the difference between the sample means divided by the standard error of the difference. In this case, the sample mean for Machine A is 6.01 and the sample mean for Machine B is 5.99. The standard error of the difference is calculated as the square root of the sum of the variances divided by the sample size. In this case, the variance for Machine A is 0.0025 and the variance for Machine B is 0.0024. The sample size is 10. Therefore, the standard error of the difference is 0.0049. The test statistic T is calculated as (6.01 - 5.99) / 0.0049 = 4.08.

Two Coffee-Vending Machines Are Studied to Determine Whether They Distribute