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13. Hypothesis testing against a two-sided alternative using the t-statistic Suppose a data set of 400 observations (N = 400) was analyzed using OLS to examine the relationship between rent and student population in college cities. The regression results are as follows, with standard errors in parentheses: log(rent) = 0.05 (0.99) + 0.7 log(pop) (0.05) - 0.007 pctstu (0.003) + 0.6 log(avginc) (0.02) where rent = average monthly rent pop = total city population avginc = average income of city residents pctstu = percentage of city population who are students R^2 = 0.498 Based on the number of observations and parameters in the model, there are 396 degrees of freedom. Suppose you want to test the null hypothesis that student population has no ceteris paribus effect on monthly rent in college cities. Since you are using a null hypothesis that ?2 = 0, your t-statistic is t = (-0.007)/(0.003) = -2.333. For the two sided alternative hypothesis ?2 ? 0 and 5% rejection rule (i.e., at the 5% level), you should compare the absolute value of your t-statistic to the critical value (?1.96). In this situation, you would reject the null hypothesis that ?2 = 0.

          13. Hypothesis testing against a two-sided alternative using the t-statistic

Suppose a data set of 400 observations (N = 400) was analyzed using OLS to examine the relationship between rent and student population in college cities. The regression results are as follows, with standard errors in parentheses:

log(rent) = 0.05 (0.99) + 0.7 log(pop) (0.05) - 0.007 pctstu (0.003) + 0.6 log(avginc) (0.02)

where
rent = average monthly rent
pop = total city population
avginc = average income of city residents
pctstu = percentage of city population who are students

R^2 = 0.498

Based on the number of observations and parameters in the model, there are 396 degrees of freedom.

Suppose you want to test the null hypothesis that student population has no ceteris paribus effect on monthly rent in college cities.
Since you are using a null hypothesis that ?2 = 0, your t-statistic is t = (-0.007)/(0.003) = -2.333.

For the two sided alternative hypothesis ?2 ? 0 and 5% rejection rule (i.e., at the 5% level), you should compare the absolute value of your t-statistic to the critical value (?1.96). In this situation, you would reject the null hypothesis that ?2 = 0.

13. Hypothesis testing against a two-sided alternative using the t-statistic

Suppose a data set of 400 observations (N = 400) was analyzed using OLS to examine the relationship between rent and student population in college cities. The regression results are as follows, with standard errors in parentheses:

log(rent) = 0.05 (0.99) + 0.7 log(pop) (0.05) - 0.007 pctstu (0.003) + 0.6 log(avginc) (0.02)

where
rent = average monthly rent
pop = total city population
avginc = average income of city residents
pctstu = percentage of city population who are students

R^2 = 0.498

Based on the number of observations and parameters in the model, there are 396 degrees of freedom.

Suppose you want to test the null hypothesis that student population has no ceteris paribus effect on monthly rent in college cities.
Since you are using a null hypothesis that ?2 = 0, your t-statistic is t = (-0.007)/(0.003) = -2.333.

For the two sided alternative hypothesis ?2 ? 0 and 5% rejection rule (i.e., at the 5% level), you should compare the absolute value of your t-statistic to the critical value (?1.96). In this situation, you would reject the null hypothesis that ?2 = 0.

Added by Lauren B.

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