Reference no: EM131763921
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.
Dependent variable is: Violent Crime
R squared = 35.6% R squared (adjusted) = 37.6%
s = 129.6 with 37 degrees of freedom
Variable Coeff SE (Coeff) t-ratio P-value
Intercept 1377.34 185.1 7.44 <0.0001
Police Officer Wage 9.42 4.139 2.28 0.0287
Graduation Rate -16.43 2.800 -5.87 <0.0001
a) State the standard null and alternative hypotheses for the true coefficient of Graduation Rate.
A. H0?:βGradRateequals=0
HA?:βGradRatenot equals≠0
B. H0?:βGradRateequals=0
HA?:βGradRategreater than>0
C. H0?:βGradRatenot equals≠0
HA?:βGradRateequals=0
D. H0?: βGradRateequals=0
HA?:βGradRateless than<0
b) What is the? t-statistic corresponding to this? test?
The? t-statistic is jQuery20009157236664776085_1512881460546??. ?(Type 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 R squared is less than? 50%.
D. The? t-statistic is negative because the coefficient has the smallest standard error.
d) What is the? P-value corresponding to this? t-statistic?
A. -0.694
B. <0.0001
C. 0.0287
D. 9.42
?e) Test the null hypothesis? (at alphaαequals=?0.05) and state your conclusion.
A. Reject Upper H0. There is insufficient evidence that the coefficient is different from 0.
B. Fail to reject Upper H0. There is insufficient evidence that the coefficient is different from 0.
C. Reject Upper H0. There is sufficient evidence that the coefficient is different from 0.
D. Fail to reject Upper H0. There is sufficient evidence that the coefficient is different from 0.
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