Suppose we wish to test for difference in population means among three groups.

a. Explain why it is not sufficient to simply look at the differences among the sample means, without taking into account the variability within each group.

b. Describe what we mean by between-sample variability and within-sample variability.

c. Which statistics measure the concepts in (b).

d. Explain how ANOVA would work in this situation. Table 6.13 contains the amount spent (in dollars) in a random sample of purchases where the payment was made by credit card, debit card, and check, respectively. Test whether the population mean amount spent differs among the three groups, using ???? = 0.05. Refer to the previous exercise. Now test whether the population mean amount spent differs among the three groups, using ???? = 0.01. Describe any conflict between your two conclusions. Suggest at least two courses of action to ameliorate the situation. TABLE 6.13 Purchase amounts for three payment methods Credit Card Debit Card Check 100 80 50 110 120 70 90 90 80 100 110 80