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Homework answers / question archive / Refer to the table below, which shows the amounts of nicotine (mg per cigarette) in king-size, 100 mm menthol, and 100 mm nonmenthol cigarettes
Refer to the table below, which shows the amounts of nicotine (mg per cigarette) in king-size, 100 mm menthol, and 100 mm nonmenthol cigarettes. The king-size cigarettes are nonfiltered, while the 100 mm menthol and the 100 mm nonmenthol cigarettes are filtered. Use a 0.05 significance level to test the claim that the three categories of cigarettes yield the same mean amount of nicotine. Given that only king size cigarettes are not filtered, do the filters appear to make a difference?
| King Size | Menthol | Filtered 100 mm Nonmenthol | |||
|---|---|---|---|---|---|
| Brand | Nicotine | Brand | Nicotine | Brand | Nicotine |
| 1 | 1.6 | 1 | 1.1 | 1 | 0.7 |
| 2 | 1.0 | 2 | 0.9 | 2 | 1.1 |
| 3 | 1.0 | 3 | 1.1 | 3 | 0.5 |
| 4 | 1.1 | 4 | 0.8 | 4 | 1.1 |
| 5 | 1.5 | 5 | 1.2 | 5 | 1.1 |
| 6 | 1.3 | 6 | 1.4 | 6 | 0.8 |
| 7 | 1.2 | 7 | 1.0 | 7 | 1.1 |
| 8 | 1.0 | 8 | 1.2 | 8 | 1.2 |
| 9 | 1.2 | 9 | 1.4 | 9 | 0.8 |
| 10 | 1.1 | 10 | 0.9 | 10 | 1.0 |
A single factor ANOVA test for the three types of cigarettes results in a p-value of 0.0370 which is less than the level of significance of 0.05.therefore, the null hypothesis that the population means are not different is rejected. The ANOVA shows there is a difference in the mean nicotine content of the three brands.
The results of the Excel Single Factor ANOVA test is shown below. Load the values for each type of cigarette into the ANOVA formula, and obtain the results.
The mean of the unfiltered king size cigarettes, 1.2, (column 4, row 5) is higher than both of the filtered cigarettes with mean values 1.1 and 0.94
(column 4, rows 6 - 7), so, it appears that the filters make a difference.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | |
|---|---|---|---|---|---|---|---|
| 1 | Anova: Single Factor | ||||||
| 2 | |||||||
| 3 | SUMMARY | ||||||
| 4 | Groups | Count | Sum | Average | Variance | ||
| 5 | Nicotine-King | 10 | 12 | 1.2 | 0.0444 | ||
| 6 | Nicotine-Menthol | 10 | 11 | 1.1 | 0.0422 | ||
| 7 | Nicotine- -Non Menthol | 10 | 9.4 | 0.94 | 0.0516 | ||
| 8 | |||||||
| 9 | |||||||
| 10 | ANOVA | ||||||
| 11 | Source of Variation | SS | df | MS | F | P-value | F crit |
| 12 | Between Groups | 0.344 | 2 | 0.172 | 3.7331 | 0.0370 | 3.3541 |
| 13 | Within Groups | 1.244 | 27 | 0.0461 | |||
| 14 | |||||||
| 15 | Total | 1.588 | 29 |
