Question

Recidivism refers to the return to prison of a prisoner who has been released or paroled. The data that follow reports the group median age at which a prisoner was released from a federal prison and the percentage of those arrested for another crime. Use the MS Excel printout to answer the questions that follow. (Use the exact values found in the Excel output.) egin{tabular}{l|lllllll} Group Median Age (x) & 22 & 27 & 32 & 37 & 42 & 47 & 52 \ hline % Arrested (y) & 65.8 & 58.4 & 52 & 49.7 & 45.6 & 38.6 & 22.6 end{tabular} SUMMARY OUTPUT egin{tabular}{|l|l|} hline multicolumn{2}{|c|}{ Regression Statistics } \ hline Multiple R & 0.9654 \ hline R Square & 0.9320 \ hline Adjusted R Square & 0.9184 \ hline Standard Error & 4.0088 \ hline Observations & 7.0000 \ hline end{tabular} ANOVA egin{tabular}{|l|l|c|l|l|l|} hline & df & SS & MS & F & Significance F \ hline Regression & 1 & 1101.263 & 1101.263 & 68.528 & 0.000 \ hline Residual & 5 & 80.351 & 16.070 & & \ hline Total & 6 & 1181.614 & & & \ hline end{tabular} egin{tabular}{|l|l|l|l|l|l|l|} hline & Coefficients & Standard Error & t Stat & P-value & Lower 95% & Upper 95% \ hline Intercept & 93.9371 & 5.807 & 16.176 & 0.000 & 79.009 & 108.865 \ hline x & -1.2543 & 0.152 & -8.278 & 0.000 & -1.644 & - \ hline end{tabular} (a) Find the least-squares line relating the percentage arrested to the group median age. (hat{y}=) (b) Do the data provide sufficient evidence to indicate that x and y are linearly related? Test using the t statistic at the 5% level of significance. State the null and alternative hypotheses. (H_{0}: eta=0) versus (H_{a}: eta<0) (H_{0}: eta=0) versus (H_{a}: eta>0) (H_{0}: eta<0) versus (H_{a}: eta>0) (H_{0}: eta=0) versus (H_{a}: eta eq 0) (H_{0}: eta eq 0) versus (H_{a}: eta=0) Find the test statistic. (t=) Find the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) (t>) (t<) State your conclusion. (H_{0}) is not rejected. We conclude that (eta=0). That is, x is useful in the prediction of y. (H_{0}) is rejected. We conclude that (eta eq 0). That is, x is useful in the prediction of y. (H_{0}) is not rejected. We conclude that (eta=0). That is, x is not useful in the prediction of y. (H_{0}) is rejected. We conclude that (eta eq 0). That is, x is not useful in the prediction of y. (c) Construct a 95% confidence interval for the slope of the line. (Round your answer to three decimal places.) to (d) Find the coefficient of determination, (r^{2}). (r^{2}=)

          Recidivism refers to the return to prison of a prisoner who has been released or paroled. The data that follow reports the group median age at which a prisoner was released from a federal prison and the percentage of those arrested for another crime. Use the MS Excel printout to answer the questions that follow. (Use the exact values found in the Excel output.)
egin{tabular}{l|lllllll}
Group Median Age (x) & 22 & 27 & 32 & 37 & 42 & 47 & 52 \
hline % Arrested (y) & 65.8 & 58.4 & 52 & 49.7 & 45.6 & 38.6 & 22.6
end{tabular}
SUMMARY OUTPUT
egin{tabular}{|l|l|}
hline multicolumn{2}{|c|}{ Regression Statistics } \
hline Multiple R & 0.9654 \
hline R Square & 0.9320 \
hline Adjusted R Square & 0.9184 \
hline Standard Error & 4.0088 \
hline Observations & 7.0000 \
hline
end{tabular}
ANOVA
egin{tabular}{|l|l|c|l|l|l|}
hline & df & SS & MS & F & Significance F \
hline Regression & 1 & 1101.263 & 1101.263 & 68.528 & 0.000 \
hline Residual & 5 & 80.351 & 16.070 & & \
hline Total & 6 & 1181.614 & & & \
hline
end{tabular}
egin{tabular}{|l|l|l|l|l|l|l|}
hline & Coefficients & Standard Error & t Stat & P-value & Lower 95% & Upper 95% \
hline Intercept & 93.9371 & 5.807 & 16.176 & 0.000 & 79.009 & 108.865 \
hline x & -1.2543 & 0.152 & -8.278 & 0.000 & -1.644 & - \
hline
end{tabular}
(a) Find the least-squares line relating the percentage arrested to the group median age.
(hat{y}=)
(b) Do the data provide sufficient evidence to indicate that x and y are linearly related? Test using the t statistic at the 5% level of significance.
State the null and alternative hypotheses.
(H_{0}: eta=0) versus (H_{a}: eta<0)
(H_{0}: eta=0) versus (H_{a}: eta>0)
(H_{0}: eta<0) versus (H_{a}: eta>0)
(H_{0}: eta=0) versus (H_{a}: eta 
eq 0)
(H_{0}: eta 
eq 0) versus (H_{a}: eta=0)
Find the test statistic.
(t=)
Find the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)
(t>)
(t<)
State your conclusion.
(H_{0}) is not rejected. We conclude that (eta=0). That is, x is useful in the prediction of y.
(H_{0}) is rejected. We conclude that (eta 
eq 0). That is, x is useful in the prediction of y.
(H_{0}) is not rejected. We conclude that (eta=0). That is, x is not useful in the prediction of y.
(H_{0}) is rejected. We conclude that (eta 
eq 0). That is, x is not useful in the prediction of y.
(c) Construct a 95% confidence interval for the slope of the line. (Round your answer to three decimal places.)
to
(d) Find the coefficient of determination, (r^{2}).
(r^{2}=)

$Recidivism refers to the return to prison of a prisoner who has been released or paroled. The data that follow reports the group median age at which a prisoner was released from a federal prison and the percentage of those arrested for another crime. Use the MS Excel printout to answer the questions that follow. (Use the exact values found in the Excel output.) egintabularl|lllllll Group Median Age (x) 22 27 32 37 42 47 52 hline % Arrested (y) & 65.8 & 58.4 & 52 & 49.7 & 45.6 & 38.6 & 22.6 endtabular SUMMARY OUTPUT egintabular|l|l| hline multicolumn2|c| Regression Statistics hline Multiple R 0.9654 hline R Square 0.9320 hline Adjusted R Square 0.9184 hline Standard Error 4.0088 hline Observations 7.0000 hline endtabular ANOVA egintabular|l|l|c|l|l|l| hline df SS MS F Significance F hline Regression 1 1101.263 1101.263 68.528 0.000 hline Residual 5 80.351 16.070 hline Total 6 1181.614 hline endtabular egintabular|l|l|l|l|l|l|l| hline Coefficients Standard Error t Stat P-value Lower 95% & Upper 95% \ hline Intercept 93.9371 5.807 16.176 0.000 79.009 108.865 hline x -1.2543 0.152 -8.278 0.000 -1.644 - hline endtabular (a) Find the least-squares line relating the percentage arrested to the group median age. (haty=) (b) Do the data provide sufficient evidence to indicate that x and y are linearly related? Test using the t statistic at the 5% level of significance. State the null and alternative hypotheses. (H0: eta=0) versus (Ha: eta<0) (H0: eta=0) versus (Ha: eta>0) (H0: eta<0) versus (Ha: eta>0) (H0: eta=0) versus (Ha: eta eq 0) (H0: eta eq 0) versus (Ha: eta=0) Find the test statistic. (t=) Find the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) (t>) (t<) State your conclusion. (H0) is not rejected. We conclude that (eta=0). That is, x is useful in the prediction of y. (H0) is rejected. We conclude that (eta eq 0). That is, x is useful in the prediction of y. (H0) is not rejected. We conclude that (eta=0). That is, x is not useful in the prediction of y. (H0) is rejected. We conclude that (eta eq 0). That is, x is not useful in the prediction of y. (c) Construct a 95% confidence interval for the slope of the line. (Round your answer to three decimal places.) to (d) Find the coefficient of determination, (r^2). (r^2=)$

Added by Wade D.

Question

Please give Ace some feedback