Data were gathered from a simple random sample of cities. The variables are Viol
ID: 3208745 • Letter: D
Question
Data were gathered from a simple random sample of cities. The variables are Violent Crime (crimesper 100,000 p answer the Regression table.
Dependent variable is: Violent Crime
R squared=36.4% R squared (adjusted = 38.5%
s= 129.6 with 37 degrees of freedom
Variable
Coeff
SE (Coeff)
t-ratio
P-value
Intercept
1395.18
181.3
7.70
less than<
0.0001
Police Officer Wage
9.14
4.256
2.15
0.0384
Graduation Rate
16.43
2.800
5.87
less than<
0.0001
a) State the standard null and alternative hypotheses for the true coefficient of Graduation Rate.
A. H0: GradRate 0 HA: GradRate = 0 B. H0: GradRate = 0 HA: GradRate >0
C. H0: GradRate = 0 HA: GradRate < 0 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 R squared (adjusted) is less than 50%.
B.The t-statistic is negative because the coefficient is negative.
C.The t-statistic is negative because the coefficient has the smallest standard error.
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. 0.0384
B. <0.0001
C. 9.14
D. 0.602
e) Test the null hypothesis (at =0.05) and state your conclusion.
A.Reject H0. There is sufficient evidence that the coefficient is different from 0.
B.Reject H0. There is insufficient evidence that the coefficient is different from 0.
C. Fail to reject H0. There is sufficient 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
1395.18
181.3
7.70
less than<
0.0001
Police Officer Wage
9.14
4.256
2.15
0.0384
Graduation Rate
16.43
2.800
5.87
less than<
0.0001
Explanation / Answer
a) The null hypothesis is that beta is zero and has no effect and the alternate hypothesis is that beta of the independent variable has a signifcant effect on the dependent variable This is bet expalined by D. H0: GradRate = 0 HA: GradRate 0, hence D
b) As can be read from the table the t ratio of the table is -5.87 for graduation rate
c) The negative t value means that the coefficient is negative , hence the correct answer is b
d) as can be read from the table , the p value is
less than<
0.0001 , hence the correct answer is B
e) as the p value is less than 0.05 , we can reject the null hypothesis in favor of alternate hypothesis. As a thumb rule , if the p value is less than 0.05 than we reject the null hypothesis and if it is not less than 0.05 then we fail to reject the null hypothesis . Hence the correct answer is
.Reject H0. There is sufficient evidence that the coefficient is different from 0. A
less than<
0.0001 , hence the correct answer is B
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