Chapter 10.2, Problem 52E

(a)

To determine

To state appropriate hypotheses for performing a significance test.

Answer to Problem 52E

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 time to eat ice cream for males.

  ${\mu }_2=$ the true mean time to eat ice cream for females.

(b)

To determine

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

Answer to Problem 52E

All conditions are not met.

Explanation of Solution

There are three conditions to be satisfied:

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

Independent: It is satisfied because the sample of $29$ male students is less than $10\%$ of the population of all male students and the sample of $35$ female students is less than $10\%$ of the population of all female students.

Normal: It is not satisfied because the sample for male student is small and the distribution of males is not approximately Normal as the pattern in the dot plot is 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.