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:
$\begin{array}{ccc}\hline \text { Specimen } & \mathrm{A} & \mathrm{B} \\\hline 1 & 14.89 & 14.89 \\2 & 13.06 & 13.07 \\3 & 14.49 & 14.49 \\4 & 13.25 & 13.23 \\5 & 10.18 & 10.14 \\6 & 7.58 & 7.57 \\\hline\end{array}$

State the null and alternate hypotheses.

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:
$\begin{array}{ccc}
\hline \text { Specimen } & \mathrm{A} & \mathrm{B} \
\hline 1 & 14.89 & 14.89 \
2 & 13.06 & 13.07 \
3 & 14.49 & 14.49 \
4 & 13.25 & 13.23 \
5 & 10.18 & 10.14 \
6 & 7.58 & 7.57 \
\hline
\end{array}$

State the null and alternate hypotheses.
A) $H _ { 0 } : \mu _ { d } > 0 , H _ { 1 } : \mu _ { d } < 0$
B) $H _ { 0 } : \mu _ { d } = 0 , H _ { 1 } : \mu _ { d } \neq 0$
C) $H _ { 0 } : \mu _ { d } = 0 , H _ { 1 } : \mu _ { d } < 0$
D) $H _ { 0 } : \mu _ { d } = 0 , H _ { 1 } : \mu _ { d } = 0.01$

Quizplus · Accepted Answer

The null hypothesis ($H_0$) typically states that there is no effect or no difference, which in this context means there is no systematic difference between the weights obtained with the two balances, so $\mu_d = 0$. The alternative hypothesis ($H_1$) is that there is a difference (either more or less), so $\mu_d \neq 0$.

In an Experiment to Determine Whether There Is a Systematic