Question

Please use the following information for Questions 2, 3, and 4.

To determine whether there was a relationship between the region of the world that you live in and the amount of beer that you drink, suppose we took 3 samples of 25 people per region from Asia, Europe and America.

2) If we let µ₁, µ₂, and µ₃ be the average calcium intake per day in milligrams for people with diagnosed osteopenia, osteoporosis or neither (healthy controls), respectively, the appropriate hypotheses in this case are:

a) H₀: μ₁ = μ₂ = μ₃

H_a: μ₁, μ₂, μ₃, are not all equal

b) H₀: μ₁, μ₂, μ₃, are not all equal

H_a: μ₁ = μ₂ = μ₃

c) H₀: μ₁ ≠ μ₂ ≠ μ₃

H_a: μ₁ = μ₂ = μ₃

d) None of the above are correct.

3) Here are the three sample standard deviations for the calcium intake for the three groups (osteopenia, osteoporosis or neither (healthy controls)):

Column	Std. Dev.
Osteopenia	217.3
Osteoporosis	287.7
Healthy	147.2

Based on this information, do the data meet the condition of equal population standard deviations for the use of the ANOVA?

a) Yes, because 287.7 - 147.2 < 2.

b) Yes, because 287.7147.2<2287.7147.2<2.

c) No, because 287.7 - 147.2 > 2.

d) No, because the standard deviations are not equal.

4)

The analysis was run on the data and the following output was obtained:
ANOVA table

Source	df	SS	MS	F-Stat	P-value
Treatments	2	152,429.6	76,214.8	1.26	.2897
Error	72	906,533.4	60,435.6
Total	74	1,058,963.0

Based on this information, we :

a) Fail to reject the H₀ and conclude that the data do not provide sufficient evidence that there is a relationship between calcium intake and bone health.

b) Fail to reject the H₀ and conclude that the data provide strong evidence that the three means (representing calcium intake and bone health) are not all equal.

c) Reject the H₀ and conclude that the data provide strong evidence that there is a relationship between between calcium intake and bone health.

d) Reject the H₀ and conclude that the data provide strong evidence that calcium intake is related to bone health in the following way: the mean for healthy people is higher than the mean for people with Osteopenia, which in turn is higher than that for people with Osteoporosis.

Answer 1

For this problem, a good idea regarding the concept of ANOVA and distribution are needed. The problem thus has been done in a manner it can be understood from the calculation perspective too and thus I have given the necessary calculations for each answers.