Reference no: EM131231803
Question1. The U.S. Postal Service is worried about potential alcoholism among its employees. In particular, an investigation panel suggests that the stress of the job can lead to coping mechanisms such as alcohol use. The panel has gathered data from a random sample of 200 employees, 80 who hold supervisor positions (and therefore experience more stress in the workplace) and 120 who do not hold supervisor positions. They have found that 20 of the supervisors are alcoholics while 5 of the nonsupervisors are.
a. Does there appear to be a relationship between workplace position (supervisor v. nonsupervisory) and alcoholism? Explain.
b. What type of statistical test would you use to examine this relationship and why?
c. The investigation panel has heard from some employees that using the ziptronic machine (a machine that makes employees identify zip codes at a rapid pace) is quite stressful. So, the panel wants to introduce this as a potential alternative explanation for alcoholism. The panel finds that of the 20 supervisors who are alcoholics 15 of them have operated the ziptronic machine and that of the 5 nonsupervisors who are alcoholics 1 has operated the machine. Construct a controlled crosstabulation table and interpret what you find.
d. What type of graphical display would be appropriate to accompany the controlled crosstabulation table?
e. Explain how you would use statistical tests to examine the relationships between the three variables.
Question 2. A director of an MPA program is interested in graduates' success in obtaining employment in "relevant" fields within one year of graduation. She believes that MPA programs requiring quantitative research methods courses will be more successful than those that don't. She finds 76% of graduates from programs requiring research methods obtained employment while 63% of graduates from programs without the requirement did.
a. Does there appear to be a relationship? Explain.
b. What type of statistical test would you use to examine this relationship and why?
c. The director also wonders if it matters whether the program is offered through the physical classroom (traditional) or online and finds the following percentages of graduates obtaining employment: traditional, methods required = 82%; traditional, methods not required = 72%; online, methods required = 70%; online, methods not required = 60%. Construct a controlled mean comparison table to represent the data.
d. Explain what the table shows.
Question 3. Forrest Tucker, the head statistician for the National Parks Service, believes that park usage as measured by number of visitors (Y) is a function of the number of people who live within 200 miles of the park (X1), the number of camping hookups available (X2), and the mean annual temperature at the park (X3). For a sample of 200 parks under Forrest's supervision, the following regression is calculated:
Yhat = 147 + .0212X1 + 15.4X2 + 186X3
R2 = .50
Forrest also found the t-statistics and p-values for the partial slope (coefficient) estimates for X1, X2, and X3:
t-statistic p-value
X1 1.350 .068
X2 1.242 .073
X3 17.885 <.001
a. Interpret the regression results. What do you tell Forrest about the impact of each of the three variables on the number of visitors (hint: think about both statistical significance of effects and substantive impact)? What do you tell Forrest about the combined explanatory power of the three variables?
b. Forrest is curious about the impact of global warming on visitors to his parks. He asks you what will happen to the number of visitors over the next ten years if the mean annual temperature rises five degrees (holding all else constant). What do you tell him?