Chapter 10, Problem T10.13SPT

(a)

To determine

To explain to a researcher why this is a bad idea and suggest a better method of deciding when each subject receives the two treatments.

Explanation of Solution

This idea is a bad idea because by making the subject test with no coffee one day and the other subject with coffee on the next day does not allow us to see if the variable of coffee improves the scores because of the outside factor. For example, if the students may have slept better before Monday’s exam test than Wednesday’s test because of the weekend. The better method of deciding is the hypothesis testing that can give appropriate results.

(b)

To determine

To carry out an appropriate test to find whether there is convincing evidence that drinking coffee improves memory, on average.

Answer to Problem T10.13SPT

We are $95\%$ confident that having one cup of coffee does not improve memory.

Explanation of Solution

To perform a test statistics, define the hypothesis:

  $\begin{array}{l}{H}_0:{\mu }_D=0\\ H_{\alpha }:{\mu }_D>0\end{array}$

Where ${\mu }_D$ is the mean difference in score i.e. one cup minus no cup, in the table.

Since the confidence interval is not stated then we will use $c=0.05$ .

Now, we have,

  $\begin{array}{l}\overline{x}=1\\ s=0.1865\end{array}$

And the degree of freedom will be:

  $\begin{array}{l}df=10-1\\ =9\end{array}$

Thus, the test statistic value will be:

  $\begin{array}{l}t=\frac{1-0}{\frac{0.8165}{\sqrt{10}}}\\ =3.87\end{array}$

Thus the $P\text{-value}=0.0019$ .

We conclude that the $P<c=0.05$ i.e. the P -value is less than the $c=0.05$ , thus we reject the null hypothesis $H_0$ . Therefore, we have convincing evidence that having one cup of coffee does not improve memory.