Hypothesis Testing help

Question

Really have no idea where to start :(

In an experiment comparing two weight-loss regimes A and B 20 test subjects were matched into 10 pairs so that within each pair the subjects were as similar as possible. Then A was randomly allocated to one of the subjects in each pair, and then B allocated to the other. The number of kilograms lost for each person is obtained and then the ordered A−B differences for each pair (in kg) are given below in the object d, together with some summary statistics:

sort(d) [1] -0.9 -0.3 0.2 0.4 0.6 1.2 1.4 3.3 3.5 4.3

mean(d) [1] 1.37

sd(d) [1] 1.755025

By specifying and checking (with a boxplot) an appropriate normality assumption perform a formal hypothesis test of H0:“regimes the same” against H1:“regimes not the same”.

Any help is appreciated!

Answer 1

Here's some steps and rationale:

1. Make a box plot. You can do a rough check of normality by verifying that the upper and lower quartiles are approximately 0.7 standard deviations from the mean and that extreme outliers are less than 4 standard deviations from the mean. The box plot should look symmetric.
2. If the data appear normal, then calculate the t-statistic: $T=\frac{\bar X}{S}$, where we are assuming the mean difference will be zero.
3. Look up the T-value in a t-distribution table (using 9 degrees of freedom) at 0.05 significance, call this $\pm K$

If your |T|>|K|, reject the null.