Question

Does music help or hinder memory? Many students at Matt’s school claim they can think more clearly while listening to their favorite kind of music. Matt believes that music interferes with thinking clearly. To find out which is true, Matt recruits 84 volunteers and randomly assigns them to two groups. The “Music” group listens to their favorite music while playing a “match the animals” memory game. The “No Music” group plays the same game in silence. Here are some descriptive statistics for the number of turns it took

the subjects in each group to complete the game (fewer turns indicate better performance):

Matt wants to know if listening to music affects the average number of turns required to finish the memory game for students like these.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check if the conditions for performing the test are met.

Short answer

Part a) The hypotheses are:

$$\begin{gathered} H_0:{\mu }_1={\mu }_2 \\ {H}_a:{\mu }_{1}notequalto{\mu }_2 \end{gathered}$$

Part b) All condtions are met.

Step-by-step solution

Part a) Step 1: Given information

The given claim is that a difference in the means.

Part b) Explanation

We must now determine the appropriate hypotheses for performing a significance test.

As a result, the claim represents either the null hypothesis or the alternative hypothesis. According to the null hypothesis, the population proportions are equal. If the claim is the null hypothesis, then the alternative hypothesis states the inverse of the null hypothesis.

Therefore, the appropriate hypotheses for this are:

$$\begin{gathered} H_0:{\mu }_1={\mu }_2 \\ {H}_a:{\mu }_{1}notequalto{\mu }_2 \end{gathered}$$

${\mu }_1=$the true mean number of turns required to complete the memory game for music-listening students.

For students who do not listen to music, ${\mu }_2$ is the true mean number of turns required to complete the memory game.

Part b) Step 1: Explanation

There are three requirements that must be met:

It is satisfying because the samples are drawn at random from different populations.

Independent: It is satisfying because the sample of $42$people represents less than $10\%$of the total population.

Normal: It is satisfied because both samples are large, with sample sizes of at least $30.$

As a result, all of the conditions are met, and a hypothesis test for the mean difference is appropriate.