Null Hypothesis

Question 1

The Department of Human Services (DHS) has contracted with the Institute for Research on Poverty to run an experimental job training program. A group of 200 individuals are randomly selected from among the hard-core unemployed. A control group of 50 is selected at the same time. The 200 individuals in the experimental group are assigned to a program that attempts to place them in jobs. DHS has defined placement of the individual in a job for 6 months as a success. Of this group, 38 are still employed after 6 months. Of the control group, 11 are employed after 6 months. Present a hypothesis and a null hypothesis, and test them. Present a conclusion in plain English.

Internal auditors for the city of Austin, Texas, periodically analyze patterns in parking meter collections. Specifically, the auditors focus on whether daily collection totals for the city’s two collection teams are dramatically different. The auditors feel that the average daily receipt figures for each team should not be dramatically different; large differences between teams could indicate employee thefts or misreporting of receipts. The auditors ask you, as the chief statistician, to run a difference of means test on 200 randomly selected days of receipts (100 days for each team). Present a hypothesis and a null hypothesis, and conduct a difference of means test. Based on your analysis, what can you tell the auditors? (Note: The data set for this problem is posted on Blackboard.)

Question 2

A group of men and a group of women take a test which reveals that the average score of the women is higher than that of the men.  The experimenter wants to be very sure that this difference is statistically significant before claiming that women have better abilities than men and so sets the alpha (α) level for the statistical test to .001 rather than the more typical .05.  Do you see problems that may arise with this?