Homework 4 (Individual Exercise)

Homework 4 (Individual Exercise)
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Homework 4 (Individual Exercise)
Question 1:
In a press conference, the provost of a university told the public that the average GPA of their students
is 3.5. A reporter is skeptical about the provost’s statement. He surveyed a random sample of 100
students on campus. The mean GPA from the sample is 3.4 and the standard deviation is 0.4.
Please do a t-test to test the following research hypothesis. You need to first write down the null and
alternative hypotheses.
1. Whether the average GPA of the university students is equal to 3.5?
a. Research Hypotheses (H0 and Ha):
Hypothesis
H0: Mean GPA for the students is equal to 3.5
Versus
H1: Mean GPA for the students is not equal to 3.5
b. T-test:
tcalc= X −μ
sX
where sX= s
√n (d.f.=n-1)
tcalc= X −μ
s
√ n
tcalc= 3.5−3.4
0.4
√ 100
=2.5
However t0.95 , 99=2.5
It can be observed that T > t0.95 , 99 that is 1.98 < 2.05
The null hypothesis is rejected. The conclusion is that the areas with greater levels of collective
efficacy will have significantly different mean juvenile crime rate.
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tcalc= X −μ
sX
where sX= s
√n (d.f.=n-1)

Homework 4 (Individual Exercise)
c. Interpret the results using 0.05 significance level (critical value is 1.98 for two-tailed,
α=.05, d.f. = 99, and critical value is 1.66 for one-tailed, α=.05, d.f. = 99).
tcalc=2.5
However t0.95 , 99=1.98
It can be observed therefore that T > t 0.95 , 99 that is 1.98 < 2.05
The null hypothesis is not rejected. The conclusion is that the Mean GPA for the students is
equal to 3.5.
Question 2: The Human Resources department of XYZ Company wants to example the relationship
between manager characteristics and performance rating. Interpret the following regression results.
Here are variable information.
 PERFORMANCE: Performance rating for a business unit manager
 SALES: average sales for that unit
 EXPERIENCE: the number of years the manager has been in the industry
 DUMMY: =1 if the manager has an MBA, =0 if the manager has no MBA.
1. What are the dependent and independent variables?
Dependent variable: Performance
Independent variables: Sales, experience & dummy
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