A researcher wants to know if mood is affected by music. She conducts a test on a sample of 4 randomly selected adults and measures mood rating before and after being exposed to classical
Music. Test the hypothesis that mood rating improved after being exposed to classical music.
Following are the mood ratings for the four participants: $\begin{array}{|l|l|l|}\hline & \begin{array}{c}\text { Before } \\\text { exposure }\end{array} & \begin{array}{c}\text { After } \\\text { exposure }\end{array} \\\hline \text { Participant \#1 } & 4.0 & 5.0 \\\hline \text { Participant \#2 } & 5.2 & 6.0 \\\hline \text { Participant \#3 } & 3.2 & 4.0 \\\hline \text { Participant \#4 } & 4.5 & 6.2 \\\hline\end{array}$ Assume that all conditions for testing have been met. Report the null and alternative hypothesis
And p-value. At the 5% significance level, state your decision regarding the null hypothesis and
Your conclusion about the original claim. Round all values to the nearest thousandth.

Question

A researcher wants to know if mood is affected by music. She conducts a test on a sample of 4 randomly selected adults and measures mood rating before and after being exposed to classical
Music. Test the hypothesis that mood rating improved after being exposed to classical music.
Following are the mood ratings for the four participants: $\begin{array}{|l|l|l|}\hline & \begin{array}{c}
\text { Before } \
\text { exposure }
\end{array} & \begin{array}{c}
\text { After } \
\text { exposure }
\end{array} \
\hline \text { Participant \#1 } & 4.0 & 5.0 \
\hline \text { Participant \#2 } & 5.2 & 6.0 \
\hline \text { Participant \#3 } & 3.2 & 4.0 \
\hline \text { Participant \#4 } & 4.5 & 6.2 \
\hline
\end{array}$ Assume that all conditions for testing have been met. Report the null and alternative hypothesis
And p-value. At the 5% significance level, state your decision regarding the null hypothesis and
Your conclusion about the original claim. Round all values to the nearest thousandth. 
A) $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 } , \mathrm { H } _ { \mathrm { a } } : \mu _ { 1 } \neq \mu _ { 2 } ; \mathrm { p } = 0.008$; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classical music improved mood rating.
B) $\mathrm { H } _ { 0 }$ : $\mu _ { \text {difference } } = 0 , \mathrm { H } _ { \mathrm { a } } : \mu _ { \text {difference } } < 0 ; \mathrm { p } = 0.008$; Reject the null hypothesis; there is strong evidence to suggest that exposure to classical music improved mood rating.
C) $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 } , \mathrm { H } _ { \mathrm { a } } : \mu _ { 1 } < \mu _ { 2 } ; \mathrm { p } = 0.077$; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classical music improved mood rating.
D) $\mathrm { H } _ { 0 } : \mu _ { \text {difference } } = 0 , \mathrm { H } _ { \mathrm { a } } : \mu _ { \text {difference } } > 0 ; \mathrm { p } = 0.922$; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classical music improved mood rating.

Quizplus · Accepted Answer

The null hypothesis ($H_0$) is that there is no difference in mood ratings before and after exposure to classical music ($\mu_{\text{difference}} = 0$). The alternative hypothesis ($H_a$) is that mood ratings improved ($\mu_{\text{difference}} < 0$). With a p-value of 0.008, which is less than the 5% significance level, we reject the null hypothesis, suggesting strong evidence that classical music improves mood ratings.

A Researcher Wants to Know If Mood Is Affected by Music