For a sample of 20 New England cities, a sociologist studies the crime rate in e

Question

For a sample of 20 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). A portion of the regression results is shown in the accompanying table. Use Table 2 and Table 4.

Specify the sample regression equation. (Negative values should be indicated by a minus sign. Report your answers to 4 decimal places.)

Choose the appropriate hypotheses to test whether the poverty rate and the crime rate are linearly related.

At the 5% significance level, what is the conclusion to the hypothesis test?

Construct a 95% confidence interval for the slope coefficient of income. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

Using the confidence interval, determine whether income is significant in explaining the crime rate at the 5% significance level.

Choose the appropriate hypotheses to determine whether the poverty rate and income are jointly significant in explaining the crime rate.

At the 5% significance level, are the poverty rate and income jointly significant in explaining the crime rate?

For a sample of 20 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). A portion of the regression results is shown in the accompanying table. Use Table 2 and Table 4.

Explanation / Answer

(b1) H0: 1 = 0; HA: 1 0

(b2) Do not reject H0 we cannot conclude the poverty rate and the crime rate are linearly related.

Since p-value is more than alpha=0.05 or 5% level of significance

(c1) Poverty(-8.72 , 18.3) and Income(-41.71 , 36.03)

(c2) Income is not significant in explaining the crime rate, since its slope coefficient does not significantly differ from zero.

Since coefficient of Income -2.8372fall in confidence interval (-41.71 , 36.03)

(d1) H0: 1 = 2 = 0; HA: At least one j 0

(d2) Yes, since the null hypothesis is rejected.

As p-value is less than level of significance alpha=0.05=5%

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.