12.7. Refer to the previous exercise.

(a) Suppose that the first observation in the second group was actually 9, not 1. Then, the standard deviations are the same, but the sample means are 6, 7, and 8 rather than 6, 3, and 8.Do you think the F test statistic would be larger, the same, or smaller? Explain your reasoning, without doing any calculations.

(b) Suppose you had the same means as these data, but the sample standard deviations were 1.0, 1.8, and 1.6, instead of the actual 2.0, 2.8, and 2.6. Do you think the F test statistic would be larger, the same, or smaller?

Explain your reasoning.

(c) Suppose you had the same means and standard deviations as these data, but the sample sizes were 30, 20, and 30, instead of 3, 2, and 3. Do you think the F test statistic would be larger, the same, or smaller? Explain your reasoning.

(d) In (a), (b), and (c), would the P-value be larger, the same, or smaller?Why?

TABLE 12.23 How often go to bar or tavern? Very often Occasional Never Mean no. good friends Standard deviation Sample size 12.1 6.4 6.2 21.3 10.2 14.0 41 166 215 Sum of Mean Source Squares df Square F Prob>F Group 1116.8 2 558.4 3.03 0.049 Residual (Error) 77171.8 419 184.2 Total 78288.5 421