Description

Interpreting Statistical Results

For the following 6 questions, imagine that your boss has had her entire analysis staff quit in a huff, but not before they performed a bivariate regression and a multiple regression on a critical issue related to productivity and gave her the results. Your boss has heard that you have taken POS 303, and she requests your help to understand and interpret the statistical table that the team has given her. Table 1 presents the two linear regression models in question.

Your boss describes the two regressions she requested from the analysis team to you. Both of the models predict how many dollars of productivity employees created, using a 500 person random sample of her company’s thousands of employees during a week in Septem- ber. First, she wanted to know if just the years spent working at the company (Years at Company) predict higher productivity (model 1). Then, her analysis team said they should put together a model (model 2) that also included other factors that could possibly explain productivity: gender of employee (1 female, 0 male), if employee holds a university degree (1 holds university degree, 0 does not hold university degree), and a measurement of each employee’s score on a work proficiency test that runs from 1 (lowest proficiency) to 100 (highest proficiency). The team in labelled the table in a note below the regression results.

1. Setting aside ethics, based on table 1, would you tell your boss that she should (illegally) focus on hiring only men (gender=0) for the job? Why or why not, discussing the evidence you have in model 2? (5 points)
2. Your boss asks how predictive her work proficiency test is of employee productivity. She asks how many dollars the table tells you scoring 5 points higher on the exam will make the company based on this model. Show and explain the calculation you performed. (7 points)
3. Your boss also wants to know if she can trust that the relationship she finds from this random sample of her employees about work proficiency test scores will hold up in the rest of her employees who weren’t sampled. What do you tell her, and based on what evidence? (3 points)
4. Your boss is very confused that the coefficient numbers for the variable “Years at Company” are quite different from one another in the two models. Why would you tell her they are different? Based on these models, would you tell her that years of service are a key causal determinant of employee productivity? (5 points)
5. Your boss wants to know if the analysis team really needed to bother collecting the data on gender, university degree, and proficiency tests. Did it help explain more of the variation in productivity in the model? How much more and how do you know from the table? (5 points)
6. Finally, she wants to know if she should put a big priority in her hiring process on hiring candidates with a university degree. How would you answer her, and what information

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from the table would you use to inform that answer? (5 points)

Performing Statistical Analysis

For the next 14 questions, I have provided you with a dataset in bblearn, in the same folder as this test prompt file and your assignment link, called teachersalary.sav. You will perform data analysis using it to answer the following questions. It is data on teacher’s salary across 50 U.S. states and the District of Columbia in 2005-2006. It contains five variables, including:

• state, the name of the state
• salary, the average salary of teachers in that state (dollars)
• spending, the average state spending per pupil in that state (dollars)
• northeastmidwest, an indicator variable taking the value of 1 if that state is in the northeast or midwest region of the United States, 0 otherwise
• south, an indicator variable taking the value of 1 if that state is in the south region of the United States, 0 otherwise

7. What are the mean, median, and standard deviation of the variable average state spending per pupil (spending)? (5 points)
8. What does the value of the median of average state spending per pupil relative to the mean of average state spending per pupil mean about the distribution of that variable? (1 point)
9. Calculate and report the bivariate correlation (sometimes called Pearson’s correlation or Pearson’s R as well) between the variables average state spending per pupil (spend- ing) and average salary of teachers in state (salary). In words, what does this statistic mean about these two variables? (4 points)
10. Perform a difference of means t-test on the variable average salary of teachers in a state (salary) between states in the south (south=1) and states not in the south (south=0) with a null hypothesis that they have the same mean teacher salary. Do not assume equal variances. What is the p-value of that test, and, in words, what can we conclude from the test if our decision criteria is the .05 level of statistical significance for rejecting the null? (3 points)
11. Perform a difference of means t-test on the variable average state spending per pupil in state (spending) between states in the northeast or midwest (northeastmidwest=1) and states not in the northeast or midwest (northeastmidwest=0) with a null hypothesis that they have the same mean state spending per pupil. Do not assume equal variances. What is the p-value of that test, and, in words, what can we conclude from the test if our decision criteria is the .05 level of statistical significance for rejecting the null? (3 points)