In an experiment to determine whether there is a systematic difference between the weights obtained with two different mass balances, six specimens were weighed, in grams, on each balance. The following data were obtained:
$\begin{array}{crr}\hline \text { Specimen } & {\mathrm{A}} & {\mathrm{B}} \\\hline 1 & 13.05 & 13.07 \\2 & 6.38 & 6.40 \\3 & 5.00 & 4.95 \\4 & 13.33 & 13.29 \\5 & 10.56 & 10.55 \\6 & 12.92 & 12.92 \\\hline\end{array}$

State the null and alternate hypotheses.

Question

In an experiment to determine whether there is a systematic difference between the weights obtained with two different mass balances, six specimens were weighed, in grams, on each balance. The following data were obtained:
$\begin{array}{crr}
\hline \text { Specimen } & {\mathrm{A}} & {\mathrm{B}} \
\hline 1 & 13.05 & 13.07 \
2 & 6.38 & 6.40 \
3 & 5.00 & 4.95 \
4 & 13.33 & 13.29 \
5 & 10.56 & 10.55 \
6 & 12.92 & 12.92 \
\hline
\end{array}$

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

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 $\mu_d = 0$, where $\mu_d$ is the mean difference between the weights measured by the two balances. The alternative hypothesis ($H_1$) is what you test against the null hypothesis. Since we are looking to see if there is any systematic difference (either more or less), without specifying the direction of the difference, the correct alternative hypothesis is $\mu_d \neq 0$, indicating that there is a difference, but not specifying if balance A is systematically heavier or lighter than balance B.

In an Experiment to Determine Whether There Is a Systematic