Evaluating Decisions Unit 6 (7 Qtns.), Hypothesis (2 Qtns.), HIV AIDS Case (10 Qtns.) and Measure of Association PRE (2 Qtns.)

Unit 6

Evaluating Decisions

A school district has developed a teaching proficiency scale based on: (a) improvements in student achievement, (b) rating by peers and (c) ratings by administrators. The district data indicates that teachers who, at the end of their 3rd year, attain ratings of 3 or higher on the teaching proficiency scale are likely to have fewer discipline problems with students, to interact well with students’ parent and are less likely to suffer from teacher-burn-out. The state department of education requires all applicants for a teaching certification to take a nationally normed teacher certification examination. Figure 1 is a scatter plot (shown below) that shows the relationship between the teacher certification test and the 3rd year teaching proficiency scale for the last 30 teachers hired by the district. Table 1 shows the data from this group of teachers. The correlation between the teacher certification examination and the teacher proficiency scale is 0.523.

Figure 1

Table 1

Applicant Gender	Certification Test	Teacher Proficiency Scale
Male	30	1
Male	40	1
Female	45	2
Male	45	3
Female	50	3
Male	53	3
Male	55	2
Male	56	1
Female	59	1
Male	61	2
Male	63	3
Male	65	2
Male	68	1
Male	68	4
Male	70	2
Male	73	1
Female	74	4
Male	74	3
Female	75	2
Female	76	2
Female	77	3
Female	78	3
Female	78	4
Female	80	4
Female	81	1
Female	82	3
Female	85	4
Male	87	5
Female	90	5
Female	95	3

1. If a successful third year teacher is one who has a teaching proficiency of 3 or higher, what is the base rate of the teachers who are shown in Table 1 and Figure 1? (1 points)

2. The district expects to hire 20 new teachers in the coming year. The district has 40 applicants for the new positions. If the district administration uses the teaching certification examination to make their selection decision where should the cut-off be set? Assume that the performance of the new applicants will similar to the applicants shown in the 30 teachers represented in Table 1 and Figure 1. Explain your answer. (5 points) (Hint you need to calculate the new selection ratio to find the cut-off)

3. Given your recommended cut-off, what would be the expected hit rate (i.e. valid accepts) for successful new hires? (Assume success is achieving a 3 or high on the teaching proficiency scale in three years. (2 points)

4. What are the probabilities associated with all of the possible outcomes of using the state’s teacher certification test to make selection decisions. (Hint: draw a decision tree) (5 points)

5. Assign a relative outcome value to each outcome, +1 for outcomes that you believe are most valuable, -1 for outcomes that you believe are most costly, and 0 for outcomes that are neither valuable nor costly. Calculate the value of the decision strategy, and compare the value to hiring 20 teachers selected randomly from the applicant pool. (5 points)

6. What would the expected hit rate be if the district needed to hire 16 new teachers instead of 20? (2 points)

7. The school district is concerned that there may be gender bias in the decision making process. The correlation coefficient for male applicants is 0.493, and the correlation for the female applicants is 0.429. Calculate the regression formula for male and female applicants. Is there a test bias? If yes, discuss the nature of the bias and discuss how it is likely to affect the quality of decision-making processes? (10 points)