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 as follows. [You may find it useful to reference the t table.) F 0.05 ANOVA Regression Residual Total M S 229.2 4,464.56 Significance F 0.950 df SS 2 458.3 17 75,897.54 1976,355.9 Intercept Poverty Income Coefficients 754.4596 1.2189 0.8372 Standard Error 71.8177 4.1781 12.3668 t Stat p-value 10.5050 .000 0.2920 0.774 0.0680 0.947 b-1. Choose the appropriate hypotheses to test whether the poverty rate and the crime rate are linearly related. HO: B1 = 0; HA: 81 # HP: 61 2 0; HA: 61 < 0 He: B1 < 0; HA: 61 > 0

Answer 1

b1) option a)
b2) option A)

c1)

alpha,α =    0.05                  
estimated slope=   0.8372                  
std error =    12.3668                  
                      
Df = 17                  
t critical value =    2.110   [excel function: =t.inv.2t(α,df) ]              
                      
margin of error ,E = t*std error =    2.110   *   12.3668   =   26.0917  
                      
95%   confidence interval is ß1 ± E                   
lower bound = estimated slope - margin of error =    0.8372   -   26.0917   =   -25.25  
upper bound = estimated slope + margin of error =    0.8372   +   26.0917   =   26.93  

(-25.25 , 26.93)

c2) option c)
d1) option c)
d2) option a)