In Exercise 1.23, we learned of a study to determine whether just one session
of cognitive behavioral therapy can help people with insomnia. In the study,
forty people who had been diagnosed with insomnia were randomly divided into
two groups of 20 each. People in one group received a one-hour cognitive
behavioral therapy session while those in the other group received no
treatment. Three months later, 14 of those in the therapy group reported sleep
improvements while only 3 people in the other group reported improvements. (a)
Create a two-way table of the data. Include totals across and down.
(b) How many of the 40 people in the study reported sleep improvement?
(c) Of the people receiving the therapy session, what proportion reported
sleep improvements?
(d) What proportion of people who did not receive therapy reported sleep
improvements?
(e) If we use \(\hat{p}_{T}\) to denote the proportion from part (c) and use
\(\hat{p}_{N}\) to denote the proportion from part (d), calculate the difference
in proportion reporting sleep improvements, \(\hat{p}_{T}-\hat{p}_{N}\) between
those getting therapy and those not getting therapy.
