Question

A child psychologist believes that controlled physical outbursts of anger (like punching a pillow) may improve the mood of young boys with emotional impairment. He believes that the proportion of boys that would benefit from this treatment is greater than the proportion of girls. A random sample from each population receives counseling in the treatment and is asked about their mood after an episode (x is the number of test subjects that reported an improvement in mood). The results of the study are summarized in the table below.

8) (3 points) Find the percentage of children that reported an improved mood from each group. Compare the percentages between boys and girls. Do the initial (untested) findings show what the psychologist expected?

9) (4 points) Assuming the conditions for a two proportion z-test hold, state the alternative hypothesis then find the observed test statistic and p-value. Round to the nearest hundredth.

10) (3 points) State your decision regarding the null hypothesis, H0: p1 = p2. How do the test results compare to the expectations of the psychologist?

Answer 1