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

Dependent variable​ is: Violent Crime

R squared=36.1​   R squared ​(adjusted)equals=38.2%

s=129.6 with 37 degrees of freedom

Variable	Coeff	SE​ (Coeff)		​t-ratio		​P-value
Intercept	1391.86	187	.88	7.41		<	0.0001
Police Officer Wage	9.43	4	.214	2.24			0.0313
Graduation Rate	−16.47	2	.800	−5.88		<	0.0001

a) State the standard null and alternative hypotheses for the true coefficient of Graduation Rate.

A. H0​: βGradRate≠0

HA​:βGradRate=0

B.H0​: βGradRate=0

HA​: bβGradRate≠0

C.H0​: βGradRate=0

HA​: βGradRate<0

D.H0​: βGradRate=0

HA​: βGradRate>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 has the smallest standard error.

C. The​ t-statistic is negative because the coefficient is negative.

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.−0.642

B.9.43

C.0.0313

D. <0.0001

​e) Test the null hypothesis​ (at α=​0.05) and state your conclusion.

A.Reject H0. There is insufficient evidence that the coefficient is different from 0.

B.Fail to reject H0. There is insufficient evidence that the coefficient is different from 0.

C.Reject H0.There is sufficient evidence that the coefficient is different from 0.

D.Fail to reject H0.There is sufficient evidence that the coefficient is different from 0.

Answer 1

a) State the standard null and alternative hypotheses for the true coefficient of Graduation Rate.

Ans:

B.

H0 : β_GradRate=0

HA : β_GradRate≠0

b) What is the t-statistic corresponding to this test?

Ans: The t-statistic is -5.88 (a decimal.)

c) Why is the t-statistic negative?

Ans: C. The t-statistic is negative because the coefficient is negative.

d) What is the P-value corresponding to this t-statistic?

Ans: D. <0.0001

e) Test the null hypothesis (at α= 0.05) and state your conclusion.

Ans:

C. Reject H0. There is sufficient evidence that the coefficient is different from 0.