. ttest death if pm10winter==1 | pm10winter==5, unequal by (pm10winter)

Two-sample t test with unequal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. err. Std. dev. [95% conf. interval] ---------+-------------------------------------------------------------------- 1 | 111 22.20721 .5019401 5.288267 21.21248 23.20193 5 | 110 21.35455 .5105372 5.35456 20.34268 22.36641 ---------+-------------------------------------------------------------------- Combined | 221 21.78281 .3582941 5.326424 21.07668 22.48893 ---------+-------------------------------------------------------------------- diff | .8526618 .7159554 -.5583864 2.26371 ------------------------------------------------------------------------------ diff = mean(1) - mean(5) t = 1.1909 H0: diff = 0 Satterthwaite's degrees of freedom = 218.898

Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.8825 Pr(|T| > |t|) = 0.2350 Pr(T > t) = 0.1175

summarize death if pm10winter==1

Variable | Obs Mean Std. dev. Min Max -------------+--------------------------------------------------------- death | 111 22.20721 5.288267 12 37

. summarize death if pm10winter==5

Variable | Obs Mean Std. dev. Min Max -------------+--------------------------------------------------------- death | 110 21.35455 5.35456 8 35

test the null hypothesis that the mean mortality is the same regardless of the pollution level by comparing the mean mortality in the lowest and highest pollution strata. Given the large sample sizes, there is no need to pool the variances.

• calculate by hand a 95% confidence interval for the truemean mortality difference between the lowest and highest pollutiondays. show the mean mortality on low pollution days and its interval estimate, the mean mortality on high pollution days and its interval estimate, and the difference in mean mortality with interval estimate for the difference in mean mortality between low and high pollutiondays.