Consider the data from Exercise 6.7.11. Given that there are only a small number of observations in

each group, the confidence interval calculated in Exercise 6.7.11 is only valid if the underlying populations

are normally distributed. Is the normality condition reasonable here? Support your answer with appropriate graphs.

Exercise 6.7.11:

Researchers were interested in the short-term effect that caffeine has on heart rate. They enlisted a

group of volunteers and measured each person’s resting heart rate.Then they had each subject drink 6 ounces of coffee. Nine of the subjects were given coffee containing caffeine and 11 were given decaffeinated coffee. After 10 minutes each person’s heart rate was measured again. The data in the table show the change in heart

rate; a positive number means that heart rate went up and a negative number means that heart rate went down.⁴⁶

 

(a) Use these data to construct a 90% confidence interval for the difference in mean affect that caffeinated

coffee has on heart rate, in comparison to decaffeinated coffee. [Note: Formula (6.7.1) yields 17.3

degrees of freedom for these data.]

(b) Using the interval computed in part (a) to justify your answer, is it reasonable to believe that caffeine

may not affect heart rates?

(c) Using the interval computed in part (a) to justify your answer, is it reasonable to believe that caffeine

may affect heart rates? If so, by how much?

(d) Are your answers to (b) and (c) contradictory? Explain.

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: