# Suppose we have data on the number of U.S. recruits who were rejected for service in a war against Spain

###### Question:

Suppose we have data on the number of U.S. recruits who were rejected for service in a war against Spain
because they did not have enough teeth. We wish to compare the rejection rate for recruits who were under
the age of 20 with the rate for those who were 40 or over. To run a logistic regression for this setting, we
define an indicator explanatory variable x with values 0 for age under 20 and 1 for age 40 or over. The
following gives output for this analysis:

Predictor Coef SE (Coef) Z p
Constant -6.76382 0.121316 -55.75 0.000
Age 4.41058 0.122498 36.01 0.000

a) (2 points) Write the fitted logistic regression model.
b) (2 points) Using the information provided in the output, calculate and interpret the 95% confidence
interval for the regression slope.
c) (3 points) Describe and interpret the results of the significance test for the regression slope. Be sure to
give the null and alternative hypotheses, and the p-value with your conclusion.
d) (2 points) Give the odds ratio for the age parameter.
e) (2 points) Give the 95% confidence interval for the odds ratio.
f) (2 points) Give a brief description of the meaning of the odds ratio in this analysis.

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