In an experiment to determine whether there is a systematic difference between the weigh obtained with two different mass balances, six specimens were weighed, in grams, on eac balance. The following data were obtained:
$\begin{array}{crr}
\hline \text { Specimen } & {\mathrm{A}} & {\mathrm{B}} \
\hline 1 & 6.05 & 6.01 \
2 & 8.00 & 8.02 \
3 & 13.45 & 13.43 \
4 & 7.47 & 7.48 \
5 & 6.53 & 6.52 \
6 & 14.38 & 14.38 \
\hline
\end{array}$

State a conclusion using the $\alpha = 0.05$ level of significance.
A) Do not reject $\mathrm { H } _ { 0 }$. There is insufficient evidence to conclude that the mean difference differs from zero.
B) Reject $H _ { 0 }$. The mean difference appears to differ from zero.

Question

In an experiment to determine whether there is a systematic difference between the weigh obtained with two different mass balances, six specimens were weighed, in grams, on eac balance. The following data were obtained:
$\begin{array}{crr}
\hline \text { Specimen } & {\mathrm{A}} & {\mathrm{B}} \
\hline 1 & 6.05 & 6.01 \
2 & 8.00 & 8.02 \
3 & 13.45 & 13.43 \
4 & 7.47 & 7.48 \
5 & 6.53 & 6.52 \
6 & 14.38 & 14.38 \
\hline
\end{array}$

State a conclusion using the $\alpha = 0.05$ level of significance.
A) Do not reject $\mathrm { H } _ { 0 }$. There is insufficient evidence to conclude that the mean difference differs from zero.
B) Reject $H _ { 0 }$. The mean difference appears to differ from zero.

Quizplus · Accepted Answer

To determine if there is a systematic difference between the weights obtained with two different mass balances, a paired t-test can be used. The null hypothesis ($H_0$) in this context is that there is no difference in the mean weights measured by the two balances. The data provided does not show significant differences between the weights measured by balance A and balance B for each specimen. Without calculating the exact p-value, the differences are small and do not suggest a systematic bias that would lead to rejecting $H_0$ at the $\alpha = 0.05$ level of significance. Therefore, there is insufficient evidence to conclude that the mean difference differs from zero, and $H_0$ should not be rejected.

In an Experiment to Determine Whether There Is a Systematic