Consider the experiment described in Exercise 6.7.9. For the same subjects, the change in diastolic blood pressure was 1.1 mm Hg greater, on average, for the subjects on the fruits-and-vegetables diet than for subjects on the standard diet. A 97.5% confidence interval for the difference between the two population means is  . Interpret this confidence interval. That is, explain what the numbers in the interval mean. (See

Examples 6.7.1 and 6.7.3.)

Example 6.7.1:

Fast Plants The Wisconsin Fast Plant, Brassica campestris, has a very rapid growth cycle that makes it particularly well suited for the study of factors that affect plant growth. In one such study, seven plants were treated with the substance Ancymidol (ancy) and were compared to eight control plants that were given ordinary water. Heights of all of the plants were measured, in cm, after 14 days of growth.³⁹The data are given in Table 6.7.1. Parallel dotplots and normal probability plots (Figure 6.7.1) show that both

sample distributions are reasonably symmetric and bell shaped. Moreover, we would expect that a distribution of plant heights might well be normally distributed, since height distributions often follow a normal curve. The dotplots show that the ancy distribution is shifted down a bit from the control distribution; the difference in sample means is  .The SE for the difference in sample means is

Figure 6.7.1:

Example 6.7.3:

Thorax Weight Biologists have theorized that male Monarch butterflies have, on average, a larger thorax than do females.A sample of seven male and eight female Monarchs yielded the data in Table 6.7.2, which are displayed in Figure 6.7.2. (These data come from another part of the study described in Example 6.1.1.) For the data in Table 6.7.2, the SE for is

For a 95% confidence interval the multiplier is . (We could round the degrees of freedom to 12, in which case the multiplier t is 2.179. This change

Figure 6.7.2: