For a sample of 30 Australian cities, a sociologist studies the crime rate in each city (crime per 100,000 residents) as a function of its poverty rate (in %) and its average income (in $1,000). A portion of the regression results shows that the coefficients for poverty and average income are 54.22 and 5.10, respectively. Based on this information, the alternative hypothesis that X1 has significant effect on Y should be stated as follows. Note: Y = crime rate in each city (crime per 100,000 residents); X1 = poverty rate (in %); and X2 = average income (in $1,000). a. β1 < 0 b. β2 ≠ 0 c. β1 ≠ 0 d. β1 > 0
Question
For a sample of 30 Australian cities, a sociologist studies the crime rate in each city (crime per 100,000 residents) as a function of its poverty rate (in %) and its average income (in 1,000).
a.
β1 < 0
b.
β2 ≠ 0
c.
β1 ≠ 0
d.
β1 > 0
Solution
The alternative hypothesis that X1 (poverty rate) has a significant effect on Y (crime rate) would be stated as:
c. β1 ≠ 0
This hypothesis suggests that the coefficient for poverty rate (β1) is not equal to zero, meaning that there is a significant relationship between the poverty rate and the crime rate. If β1 were equal to zero, it would mean that changes in the poverty rate have no effect on the crime rate.
Similar Questions
For a sample of 30 Australian cities, a sociologist studies the crime rate in each city (crime per 100,000 residents) as a function of its poverty rate (in %) and its average income (in $1,000). A portion of the regression results shows that the coefficients for poverty and average income are 54.22 and 5.10, respectively. Based on this information, what is the value of test statistic used to test the null hypothesis that X1 has no significant effect on Y at the 5% level of significance, if the standard error of the slope of Y with variable X1 equals 15.50. Round your final answer to two decimal places. Note: Y = crime rate in each city (crime per 100,000 residents); X1 = poverty rate (in %); and X2 = average income (in $1,000).
For a sample of 40 Australian cities, a sociologist studies the crime rate in each city (crime per 100,000 residents) as a function of its poverty rate (in %) and its average income (in $1,000). A portion of the regression results shows that the coefficients for poverty and average income are 54.22 and 5.10, respectively. Based on this information, what is the upper critical value used to test the null hypothesis that X1 has no significant effect on Y at the 1% level of significance? Note: Y = crime rate in each city (crime per 100,000 residents); X1 = poverty rate (in %); and X2 = average income (in $1,000).
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