Question

Chicken diet and weight. In previous chapter, we compared the effects of two types of feed at a time. A better analysis would first consider all feed types at once: casein, horsebean, linseed, meat meal, soybean, and sunflower. The ANOVA output below can be used to test for differences between the average weights of chicks on different diets.

	DF	Sum Sq	Mean Sq	F value	Pr(>F)
feed	5	231129.16	46225.83	15.36	0.0000
residuals	65	195556.02	3008.55

Conduct a hypothesis test to determine if these data provide convincing evidence that the average weight of chicks varies across some (or all) groups. Make sure to check relevant conditions. Figures and summary statistics are shown below.

	Mean	SD	n
casein	323.58	64.43	12
horsebean	160.2	38.63	10
linseed	218.75	52.24	12
meatmeal	276.91	64.9	11
soybean	246.43	54.13	14
sunflower	328.92	48.84	12

What are the hypotheses for this test?

• Ho: μ_c = μ_h = μ_l = μ_m = μ_soy = μ_sun
  Ha: μ_c ≠ μ_h ≠ μ_l ≠ μ_m ≠ μ_soy ≠ μ_sun
• Ho: μ_c = μ_h = μ_l = μ_m = μ_soy = μ_sun
  Ha: At least one pair of means is the same
• Ho: μ_c = μ_h = μ_l = μ_m = μ_soy = μ_sun
  Ha: At least one of the means is different

The test statistic for the hypothesis test is:  (please round to two decimal places)
The p-value for the hypothesis test is:  (please round to four decimal places)
Interpret the result of the hypothesis test in the context of the study:

• Since p < α, we reject the null hypothesis and accept that the average weight of chicks is different for each type of diet
• Since p = 0, there is no chance that the average weight of chicks is the same across all of the diets
• Since p < α, we reject the null hypothesis and accept that the average weight of chicks is the same across all of the diets
• Since p < α, we reject the null hypothesis and accept that the average weight of chicks is not the same across all of the diets

Answer 1

Given

ANOVA output is:

DF	Sum Sq	Mean Sq	F value	Pr(>F)
feed	5	231129.16	46225.83	15.36	0.0000
residuals	65	195556.02	3008.55

By observing above output

The hypothesis is

Ho: μ_c = μ_h = μ_l = μ_m = μ_soy = μ_sun
Ha: At least one of the mean is different

we obtain F - value = 15.36

P - value = 0.0000

Since p < α, we reject the null hypothesis and accept that the average weight of chicks is not the same across all of the diets

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