Announcements

Differences between groups

\[ (\bar X_1 - \bar X_2) / \sqrt{\frac{S_1^2}{n_1} + \frac{S_2^2}{n_2}} \] - This has a \(t\)-distribution with degrees of freedom given by a complicated formula - The equal variances/paired cases have slightly different formulas - Don’t worry, software takes care of details pretty much automatically - Does the formula make sense? If the groups have the same mean, the observed value should be close to 0

Relation to intervals

Testing for independence

nrow(survey) # survey of this many students
## [1] 237
counts <- table(survey$Exer, survey$Sex)
counts
##       
##        Female Male
##   Freq     49   65
##   None     11   13
##   Some     58   40
chisq.test(counts)
## 
##  Pearson's Chi-squared test
## 
## data:  counts
## X-squared = 5.7184, df = 2, p-value = 0.05731