For a sample of 20 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents)
Posted: Mon Jul 11, 2022 11:28 am
For a sample of 20 New England cities, a sociologist studies thecrime rate in each city (crimes per 100,000 residents) as afunction of its poverty rate (in %) and its median income (in$1,000s). A portion of the regression results is asfollows. (You may find it useful to referencethe t table.)
b-1. Choose the appropriate hypotheses todetermine whether the poverty rate and income are jointlysignificant in explaining the crime rate.
multiple choice 1
H0: β1 = β2 =0; HA: At leastone βj > 0
H0: β1 = β2 =0; HA: At leastone βj < 0
H0: β1 = β2 =0; HA: At leastone βj ≠ 0
b-2. At the 5% significance level, are thepoverty rate and income jointly significant in explaining the crimerate?
multiple choice 2
Yes, since the null hypothesis is rejected.
Yes, since the null hypothesis is not rejected.
No, since the null hypothesis is rejected.
No, since the null hypothesis is not rejected.
c-1. Choose the appropriate hypotheses totest whether the poverty rate and the crime rate are linearlyrelated.
multiple choice 3
H0: β1 ≥0; HA: β1 <0
H0: β1 =0; HA: β1 ≠0
H0: β1 ≤0; HA: β1 >0
c-2. At the 5% significance level, what isthe conclusion to the test?
multiple choice 4
Reject H0; we can conclude the povertyrate and the crime rate are linearly related.
Reject H0; we cannot conclude thepoverty rate and the crime rate are linearly related.
Do not reject H0; we can conclude thepoverty rate and the crime rate are linearly related.
Do not reject H0; we cannot concludethe poverty rate and the crime rate are linearly related.
d-1. Construct the 95% confidence intervalfor the slope coefficient of income. (Negative valuesshould be indicated by a minus sign. Round final answers to 2decimal places.)
d-2. Using the confidence interval,determine whether income influences the crime rate at the 5%significance level.
multiple choice 5
Income is significant in explaining the crime rate, since itsslope coefficient significantly differs from zero.
Income is not significant in explaining the crime rate, sinceits slope coefficient significantly differs from zero.
Income is significant in explaining the crime rate, since itsslope coefficient does not significantly differ from zero.
Income is not significant in explaining the crime rate, sinceits slope coefficient does not significantly differ from zero.
b-1. Choose the appropriate hypotheses todetermine whether the poverty rate and income are jointlysignificant in explaining the crime rate.
multiple choice 1
H0: β1 = β2 =0; HA: At leastone βj > 0
H0: β1 = β2 =0; HA: At leastone βj < 0
H0: β1 = β2 =0; HA: At leastone βj ≠ 0
b-2. At the 5% significance level, are thepoverty rate and income jointly significant in explaining the crimerate?
multiple choice 2
Yes, since the null hypothesis is rejected.
Yes, since the null hypothesis is not rejected.
No, since the null hypothesis is rejected.
No, since the null hypothesis is not rejected.
c-1. Choose the appropriate hypotheses totest whether the poverty rate and the crime rate are linearlyrelated.
multiple choice 3
H0: β1 ≥0; HA: β1 <0
H0: β1 =0; HA: β1 ≠0
H0: β1 ≤0; HA: β1 >0
c-2. At the 5% significance level, what isthe conclusion to the test?
multiple choice 4
Reject H0; we can conclude the povertyrate and the crime rate are linearly related.
Reject H0; we cannot conclude thepoverty rate and the crime rate are linearly related.
Do not reject H0; we can conclude thepoverty rate and the crime rate are linearly related.
Do not reject H0; we cannot concludethe poverty rate and the crime rate are linearly related.
d-1. Construct the 95% confidence intervalfor the slope coefficient of income. (Negative valuesshould be indicated by a minus sign. Round final answers to 2decimal places.)
d-2. Using the confidence interval,determine whether income influences the crime rate at the 5%significance level.
multiple choice 5
Income is significant in explaining the crime rate, since itsslope coefficient significantly differs from zero.
Income is not significant in explaining the crime rate, sinceits slope coefficient significantly differs from zero.
Income is significant in explaining the crime rate, since itsslope coefficient does not significantly differ from zero.
Income is not significant in explaining the crime rate, sinceits slope coefficient does not significantly differ from zero.