Data were gathered from a simple random sample of cities. The variables are Viol
ID: 3208478 • Letter: D
Question
Data were gathered from a simple random sample of cities. The variables are Violent Crime (crimes per 100,000 population), Police Officer Wage (mean $/hr), and Graduation Rate (%). Use the accompanying regression table to answer the following questions consider the coefficient of Graduation Rate. Complete parts a through e.
Regression Table
Dependent variable is: Violent Crime
R squared=38.538.5% R squared (adjusted)=40.740.7%
s=129.6 with 37 degrees of freedom
Variable
Coeff
SE (Coeff)
t-ratio
P-value
Intercept
1383.23
182.33
7.59
<
0.0001
Police Officer
9.369.36
44.245
2.20
0.0338
Graduation Rate
16.14
22.60
6.21
<
0.0001
a) State the standard null and alternative hypotheses for the true coefficient of Graduation Rate.
A. H0: GradRate=0
HA: GradRateg>0
B. H0: GradRate0
HA: GradRate=0
C. H0: GradRate=0
HA: GradRate0
D. H0: GradRate=0
HA: GradRate<0
b) What is the t-statistic corresponding to this test?
The t-statistic is.... (Type an integer or a decimal.)
c) Why is the t-statistic negative?
A. The t-statistic is negative because the coefficient has the smallest standard error.
B. The t-statistic is negative because the coefficient is negative.
C. The t-statistic is negative because R squared (adjusted) is less than 50%.
D. The t-statistic is negative because R squared is less than 50%.
d) What is the P-value corresponding to this t-statistic?
A. <0.0001
B. 9.36
C. 0.612
D. 0.0338
e) Test the null hypothesis (at =0.05) and state your conclusion.
A. Fail to reject H0. There is sufficient evidence that the coefficient is different from 0.
B. Reject H0. There is sufficient evidence that the coefficient is different from 0.
C. Reject H0. There is insufficient evidence that the coefficient is different from 0.
D. Fail to reject H0. There is insufficient evidence that the coefficient is different from 0.
Variable
Coeff
SE (Coeff)
t-ratio
P-value
Intercept
1383.23
182.33
7.59
<
0.0001
Police Officer
9.369.36
44.245
2.20
0.0338
Graduation Rate
16.14
22.60
6.21
<
0.0001
Explanation / Answer
a)
C. H0: GradRate=0
HA: GradRate0
b) From the given above output t statistic and p-value for the coeffiecient for Graduation Rates is -6.21 and 0.0001 respectively.
c) B. The t-statistic is negative because the coefficient is negative
d) What is the P-value corresponding to this t-statistic?
A. <0.0001
e)Here p-value , alpha so
B. Reject H0. There is sufficient evidence that the coefficient is different from 0
Hope it will help you. Thanks. Good luck :)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.