Please use the following information for Questions 2, 3, and4.
To determine whether there was a relationship between the regionof the world that you live in and the amount of beer that youdrink, suppose we took 3 samples of 25 people per region from Asia,Europe and America.
2) If we let µ1, µ2, and µ3 bethe average calcium intake per day in milligrams for people withdiagnosed osteopenia, osteoporosis or neither (healthy controls),respectively, the appropriate hypotheses in this case are:
a) H0: μ1 = μ2= μ3
Ha: μ1, μ2, μ3, arenot all equal
b) H0: μ1, μ2,μ3, are not all equal
Ha: μ1 = μ2 = μ3
c) H0: μ1 ≠μ2≠μ3
Ha: μ1 = μ2 = μ3
d) None of the above are correct.
3) Here are the three sample standard deviations for the calciumintake 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 ofequal population standard deviations for the use of the ANOVA?
a) Yes, because 287.7 - 147.2 < 2.
b) Yes, because287.7147.2<2287.7147.2<2.
c) No, because 287.7 - 147.2 > 2.
d) No, because the standard deviations are notequal.
4)
The analysis was run on the data and the following output wasobtained:
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 andconclude that the data do not provide sufficient evidence thatthere is a relationship between calcium intake and bone health.
b) Fail to reject the H0 andconclude that the data provide strong evidence that the three means(representing calcium intake and bone health) are not allequal.
c) Reject the H0 and conclude thatthe data provide strong evidence that there is a relationshipbetween between calcium intake and bone health.
d) Reject the H0 and conclude thatthe data provide strong evidence that calcium intake is related tobone health in the following way: the mean for healthy people ishigher than the mean for people with Osteopenia, which in turn ishigher than that for people with Osteoporosis.
