Question

Administrators at a particular correctional institution were concerned that the offenders being sentenced to their facility had particularly high levels of depression. They decided to have a sample of 65 incoming offenders complete a self-report depression scale. The particular depression scale they used is normed to have a mean of 15 in the general population. The offenders from the institution scored an average of 17 with a standard deviation of 5 over the two years that the testing was conducted.

a) What is the appropriate model of the population distribution?

b) What are the appropriate hypotheses for this analysis?

c) What is/are the critical value(s) for this test using an alpha of 0.05?

d) What is the observed value of the appropriate test statistic?

e) What is your decision regarding the stated hypotheses?

f) What is the estimated effect size using a Cohen’s d?

g) What is the 95% confidence interval around the population mean?

h) Were the administrators justified in their concerns?

Answer 1

Solution

a) What is the appropriate model of the population distribution?

Answer : One sample t test

b)

g) What is the 95% confidence interval around the population mean?

The 95% confidence interval is 15.761<μ<18.239.

h) Were the administrators justified in their concerns?

Yes, since we are rejecting the null hypothesis so we conclude that administrators concerned that the offenders being sentenced to their facility had particularly high levels of depression.