Here are the numbers from the output for number 6.
| xbar1 | xbar2 | MSW | n1 | n2 | df | |
| 23 | 28 | 4.888889 | 4 | 4 | 9 |
Using the book's method:
| a | t | L | R | |
| 0.05 | 2.262 | -8.537 | -1.463 |
So we are 95% confident that the difference between (population) mean 1 and mean 2 is between -8.537 and -1.463. Since 0 is not included in the interval, we can conclude that the difference is significant.
Using the Bonferroni adjustment to get a 95% confidence interval:
Here we need the number of possible pairwise comparisons. Since there are 3 groups, there are 3 comparisons.
| a | m | t | L | R | |
| 0.05 | 3 | 2.933 | -9.586 | -0.414 |
(NOTE: I found the value of t using =tinv(.05/3,9).)
With this method the interval is wider, but it still does not include 0.
Using the Bonferroni adjustment to get a 94% confidence interval:
Here we need the number of possible pairwise comparisons. Since there are 3 groups, there are 3 comparisons.
| a | m | t | L | R | |
| 0.06 | 3 | 2.821 | -9.411 | -0.589 |
15. This time I will only use Bonferroni adjustment method, and a 95% confidence interval. We again have m=3, since there are 3 groups.
| xbar1 | xbar2 | xbar3 | MSW | n1 | n2 | n3 | df |
| 5 | 4.5 | 6 | 0.5 | 6 | 6 | 6 | 15 |
| Comparison | a | m | t | L | R |
| 1 and 2 | 0.05 | 3 | 2.694 | -0.600 | 1.600 |
| 1 and 3 | 0.05 | 3 | 2.694 | -2.100 | 0.100 |
| 2 and 3 | 0.05 | 3 | 2.694 | -2.600 | -0.400 |
The only interval that does not include 0 is the third one, indicating that the means of groups 2 and 3 are significantly different.
18. I will again use Bonferroni adjustment method, and a 95% confidence interval. We again have m=3, since there are 3 groups.
| xbar1 | xbar2 | xbar3 | MSW | n1 | n2 | n3 | df |
| 9.95 | 14.75 | 13.5 | 13.01963 | 12 | 8 | 10 | 27 |
| Comparison | a | m | t | L | R |
| 1 and 2 | 0.05 | 3 | 2.552 | -9.003 | -0.597 |
| 1 and 3 | 0.05 | 3 | 2.552 | -7.493 | 0.393 |
| 2 and 3 | 0.05 | 3 | 2.552 | -3.118 | 5.618 |
Here only the first interval contains 0, indicating that industries 1 and 2 (banking and financial services) have different mean P/E ratios.
32. I will use the Bonferroni adjustment to build 95% confidence intervals.
| xbar1 | xbar2 | xbar3 | MSW | n1 | n2 | n3 | df |
| 17 | 20.4 | 25 | 5.092222 | 7 | 7 | 7 | 18 |
| Comparison | a | m | t | L | R |
| 1 and 2 | 0.05 | 3 | 2.639 | -6.583 | -0.217 |
| 1 and 3 | 0.05 | 3 | 2.639 | -11.183 | -4.817 |
| 2 and 3 | 0.05 | 3 | 2.639 | -7.783 | -1.417 |
None of the intervals contain 0, indicating that all differences are significant.
59. b. I will use the Bonferroni adjustment to build 95% confidence intervals.
| xbar1 | xbar2 | xbar3 | MSW | n1 | n2 | n3 | df |
| 4.25 | 5.25 | 5.75 | 1.166667 | 8 | 8 | 8 | 21 |
| Comparison | a | m | t | L | R |
| 1 and 2 | 0.15 | 3 | 2.08 | -2.123 | 0.123 |
| 1 and 3 | 0.15 | 3 | 2.08 | -2.623 | -0.377 |
| 2 and 3 | 0.15 | 3 | 2.08 | -1.623 | 0.623 |
The second interval does not contain 0, indicating that there is a significant difference between nonbrowsers and heavy browsers. There is not a significant difference between light and nonbrowsers and between light and heavy browsers.