Question
After Emily tests the differences in variances for the placebo and Formula C, she wants to test if there is a difference in the mean
After Emily tests the differences in variances for the placebo and Formula C, she wants to test if there is a difference in the mean weight gains among the three groups of mice. Her null hypothesis is that there are no differences in the weight gains regardless of the type of Formulas that were fed to the mice. The alternative hypothesis is that at least one of the formulas results in a different mean for the weight gain in the mice. The measured weight gains are shown in the table below.
Formula A | Formula B | Formula C |
40 | 47 | 51 |
32 | 42 | 41 |
42 | 49 | 44 |
36 | 46 | 46 |
39 | 44 | 49 |
Assume that all distributions are normal, the three population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05. Upon running an ANOVA: Single Factor test, she gets the following results. Fill in the blanks (round to two digits) by running your own ANOVA: Single Factor test.
Anova: Single Factor | ||||||
SUMMARY | ||||||
Groups | Count | Sum | Average | Variance | ||
Formula A | 5 | 189 | 37.8 | 15.2 | ||
Formula B | 5 | 228 | 45.6 | 7.3 | ||
Formula C | 5 | 231 | 46.2 | 15.7 | ||
ANOVA | ||||||
Source of Variation | SS | df | MS | F | P-value | F crit |
Between Groups | ? | 2 | 109.8 | ? | 0.004772 | ? |
Within Groups | 152.8 | 12 | ? | |||
Total | 372.4 | ? |
On this graph above the question marks have to be filled in as those are the blanks.
Decision: Does Emily "reject" or "fail to reject" her null hypothesis? (Write "Yes" or "No")
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