The following output from MINITAB presents the results of a hypothesis test for a population mean $\mu$.

Test of $\mathrm { mu } = 45$ vs. not $= 45$

$\begin{array}{llrccrl}
\mathrm{N} & \text { Mean } & \text { StDev } & \text { SE Mean } & 95 \% \text { CI } & \text { T } & \text { P } \
54 & 42.10 & 16.331795 & 2.222476 & (37.642247,46.557753) & -1.304851 & 0.1975
\end{array}$

What are the null and alternate hypotheses?
A) $H _ { 0 } : \mu = 45 , H _ { 1 } : \mu = 42.10$
B) $H _ { 0 } : \mu = 45 , H _ { 1 } : \mu \neq 45$
C) $H _ { 0 } : \mu = 42.10 , H _ { 1 } : \mu \neq 42.10$
D) $H _ { 0 } : \mu \neq 45 , H _ { 1 } : \mu = 45$

Question

The following output from MINITAB presents the results of a hypothesis test for a population mean $\mu$.

Test of $\mathrm { mu } = 45$ vs. not $= 45$

$\begin{array}{llrccrl}
\mathrm{N} & \text { Mean } & \text { StDev } & \text { SE Mean } & 95 \% \text { CI } & \text { T } & \text { P } \
54 & 42.10 & 16.331795 & 2.222476 & (37.642247,46.557753) & -1.304851 & 0.1975
\end{array}$

What are the null and alternate hypotheses?
A) $H _ { 0 } : \mu = 45 , H _ { 1 } : \mu = 42.10$
B) $H _ { 0 } : \mu = 45 , H _ { 1 } : \mu \neq 45$
C) $H _ { 0 } : \mu = 42.10 , H _ { 1 } : \mu \neq 42.10$
D) $H _ { 0 } : \mu \neq 45 , H _ { 1 } : \mu = 45$

Quizplus · Accepted Answer

The null hypothesis ($H_0$) always specifies a population parameter (in this case, the mean $\mu$) equal to a certain value, which is 45 here. The alternative hypothesis ($H_1$) is what we are testing against the null hypothesis. Since the test is for $\mu = 45$ vs. not $= 45$, it indicates a two-tailed test, where the alternative hypothesis is that $\mu$ is not equal to 45.

The Following Output from MINITAB Presents the Results of a Hypothesis