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 are as follows. 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.

Construct a 95% confidence interval for the slope coefficient of income. (Negative values should be indicated by a minus sign. Round intermediate calculations to 4 decimal places, "t/2,df" value to 3 decimal places, and final 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 are as follows. Use Table 2 and Table 4.

Explanation / Answer

a)

Crime = 301.62 + 53.1597 Poverty +4.9472 Income

b-1) Correct Answer: Option (A) H0: 1 = 0; HA: 1 0

b-2) Correct Answer: Option (A) Reject H0; the poverty rate and the crime rate are linearly related.

since

P-value 0.0016 which is less than alpha 0.05, we reject H0

c-1) Confidence interval of income (12.47, 22.37)

c-2) Correct answer:option (B) Income is not significant in explaining the crime rate, since its slope coefficient does not significantly differ from zero.

d-1) Correct answer: option (B) H0: 1 = 2 = 0; HA: At least one j 0

d-2) P-value (F-significant) = 9.04E-07

which is less than alpha 0.05, we reject H0

Correct answer:option (A) Yes, since the null hypothesis is rejected.

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