1. The table below represents data on a variable of interest collected from a single sample. It is known that the variable of interest has a mean of 10 and a standard deviation of 5 in the general population. A researcher is interested in testing whether the population from which this sample was selected is different from the general population.

				Data
9	7	12	5	6	4	8	11	3	7

1. What are the appropriate hypotheses for this analysis?

1. What is/are the critical value(s) for this test at a 0.05 alpha level?

1. What is the standard error of the mean?

1. What is the observed value of the appropriate test statistic?

1. What is your decision regarding the stated hypotheses?

2. The table below represents data on a variable of interest collected from a single sample. It is known that the variable of interest has a mean of 25 in the general population. A researcher is interested in testing whether the population from which this sample was selected scores higher than the general population.

				Data
27	29	32	28	33	29	31	33	28	31

1. What are the appropriate hypotheses for this analysis?

1. What is/are the critical value(s) for this test at a 0.01 alpha level?

1. What is the estimated standard error of the mean?

1. What is the observed value of the appropriate test statistic?

1. What is your decision regarding the stated hypotheses?

3. Teachers at a particular private school thought that they were doing an exceptional job. In order to determine just how good their school was doing, they decided to have 200 of their students undergo intelligence testing just prior to graduation. The particular intelligence test they used is normed to have a mean of 100 and a standard deviation of 15 in the population. The students from the private school scored an average of 97 over the three years that testing was conducted. They wanted to test whether the average score from the private school students was different than the population mean. (6 marks)

1. What is the appropriate model of the population distribution?

1. What are the appropriate hypotheses for this analysis?

1. What is/are the critical value(s) for this test using an alpha of 0.01?

1. What is the observed value of the appropriate test statistic?

1. What is your decision regarding the stated hypotheses?

1. Was the school doing an exceptional job based on their students' IQs?

4. 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 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.

1. What is the appropriate model of the population distribution?

1. What are the appropriate hypotheses for this analysis?

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

1. What is the observed value of the appropriate test statistic?

1. What is your decision regarding the stated hypotheses?

1. What is the estimated effect size using a Cohen's d?

1. What is the 95% confidence interval around the population mean?

1. Were the administrators justified in their concerns?