Chapter 10.2, Problem 54E

(a)

To determine

To state appropriate hypotheses for performing a significance test.

Answer to Problem 54E

The hypotheses is:

  $\begin{array}{l}{H}_0:{\mu }_1={\mu }_2\\ H_a:{\mu }_1\ne {\mu }_2\end{array}$

Explanation of Solution

The given claim that: difference in the means.

Now, we have to find out the appropriate hypotheses for performing a significance test.

Thus, the claim is either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportions are equal. If the null hypothesis is the claim then the alternative hypothesis states the opposite of the null hypothesis.

Therefore, the appropriate hypotheses for this is:

  $\begin{array}{l}{H}_0:{\mu }_1={\mu }_2\\ H_a:{\mu }_1\ne {\mu }_2\end{array}$

Where we have,

  ${\mu }_1=$ the true mean number of turns required to finish the memory game for students who listen to music.

  ${\mu }_2=$ the true mean number of turns required to finish the memory game for students who do not listen to music.

(b)

To determine

To check if the conditions for performing the test are met.

Answer to Problem 54E

All conditions are met.

Explanation of Solution

There are three conditions to be satisfied:

Random: It is satisfied because the samples are randomly selected from separate populations.

Independent: It is satisfied because the sample of $42$ people is less than $10\%$ of the population of all people.

Normal: It is satisfied because both the samples are large as they both have a sample size of at least $30$ .

Thus, all the conditions are satisfied and it is then appropriate to perform a hypothesis test for the mean difference.