In: Math
A pharmaceutical manufacturer wants to investigate the bioactivity of a new drug. A completely randomized single-factor experiment was conducted with three dosage levels, and the following results were obtained. Use R to run ANOVA to test if the dosage has some effects or not.
Dosage |
Observations |
|||
20g |
24 |
28 |
37 |
30 |
30g |
37 |
44 |
31 |
35 |
40g |
42 |
47 |
52 |
38 |
a. Find the test statistic.
b. Find the p-value (Please input a decimal value. Please input 0 or 0.0001 if it is smaller than 0.0001 ) .
Anova: Single Factor | ||||||
SUMMARY | ||||||
Groups | Count | Sum | Average | Variance | ||
Column 1 | 4 | 119 | 29.75 | 29.58333 | ||
Column 2 | 4 | 147 | 36.75 | 29.58333 | ||
Column 3 | 4 | 179 | 44.75 | 36.91667 | ||
ANOVA | ||||||
Source of Variation | SS | df | MS | F | P-value | F crit |
Between Groups | 450.6667 | 2 | 225.3333 | 7.0356 | 0.0145 | 4.2565 |
Within Groups | 288.25 | 9 | 32.0278 | |||
Total | 738.9167 | 11 |
the p-value for this ANOVA rounded to 6 decimal places is 0.014464.