2.3 Carrying out the test: Paired \(t\)-test

We are now ready to carry out the paired \(t\)-test to test whether the true mean difference between before and after weights is different from 0. The results of the test are as follows:

    Paired t-test

data:  anorexia$Prewt and anorexia$Postwt
t = -2.9376, df = 71, p-value = 0.004458
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -4.6399424 -0.8878354
sample estimates:
mean of the differences 

We note the following:

  • The \(p\)-value is 0.00446, which is less than 0.05, so we reject \(H_0\). That is, we have enough evidence to conclude that the difference between before and after weights is statistically significant.
  • The 95% confidence interval for \(\mu_D\) is (-4.64, -0.89), meaning we are 95% confident that the average weight gain was between 4.64 and 0.89 lbs. Since this interval does not include 0, we can reject \(H_0\).
  • The test statistic is \(t = -2.9376\)
  • The degrees of freedom is \(71\)
  • The sample mean of the paired differences is \(-2.76\).