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 
              -2.763889 

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 $-2.76$.

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These notes have been prepared by Amanda J. Shaker. The copyright for the material in these notes resides with the author named above, with the Department of Mathematics and Statistics and with La Trobe University. Copyright in this work is vested in La Trobe University including all La Trobe University branding and naming. Unless otherwise stated, material within this work is licensed under a Creative Commons Attribution-Non Commercial-Non Derivatives License CC BY-NC-ND