Chapter 10.2, Problem 51E

(a)

To determine

To state appropriate hypotheses for performing a significance test.

Answer to Problem 51E

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 sorting time of people who listen to music.

  ${\mu }_2=$ the true mean sorting time of people who do not listen to music.

(b)

To determine

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

Answer to Problem 51E

All conditions are not met.

Explanation of Solution

There are three conditions to be satisfied:

Random: It is satisfied because the volunteerswere randomly assigned to a treatment.

Independent: It is satisfied because the $19$ peopleis less than $10\%$ of the population of all people.

Normal: It is not satisfied because the sample for no music is small and the distribution of No music is not approximately Normal as the distribution is strongly skewed to the right.

Thus, all the conditions are not satisfied since the large sample condition is not satisfied and it is then not appropriate to perform a hypothesis test for the mean difference.