7.7 Confidence Intervals
Let us return to our research team that wants to investigate how a certain diet affects the blood pressure of healthy people. Since they cannot test the diet on the whole population of healthy people they have chosen a representative sample consisting of 15 persons, which is a common sample size for these types of investigations. Before the tests they measure the blood pressures of their test persons. After 15 days of diet they measure the blood pressures again. Calculating the difference between the systolic blood pressure after and before the diet for each test person, they obtain the following results (in mm Hg):
There seems to be a large variation in the results. Two persons’ blood pressures drop by as much as 14 mm Hg, but in one person there is actually an increase. What can we say about the effect of the diet based on these figures? As a first step it is always useful to display the data graphically in a diagram. Figure 7.14 shows that the drop after the diet is about 4 mm Hg for most persons. A few persons show larger drops than this, while others show no effect or even an increase. The mean difference in the sample is −5.8 mm Hg. But this is a limited sample. The interesting question is what the mean difference in blood pressure would have been in the whole population. Is it possible to be, say, 95% certain that the diet is effective?