Suppose that you theorize that the average ages of White Oaks, Quercus alba, in the following three locations. Site 1 :
Posted: Mon Nov 15, 2021 10:42 am
Suppose that you theorize that the average ages of White Oaks,
Quercus alba, in the following three locations. Site 1 : Lower
peninsula, MI, near Lake Michigan Site 2 : Upper peninsula, MI,
near Lake Superior and Site 3 : Lower peninsula, MI, near Saginaw
Bay (are not all the same). To test this theory, you take 3 simple
random samples of 35 trees from each site, and record the ages of
each White Oak in each sample.
(a) What are the hypotheses?
H0: μ1 = μ2 =
μ3 vs. Ha: At least two of the means
differ from each other.H0: μ1 =
μ2 = μ3 vs. Ha: At least
two of the means are different from the
third. H0: μ1 =
μ2 = μ3 vs. Ha: At least
one of the means is different from all the others.H0:
μ1 = μ2 = μ3;
Ha: μ1 ≠ μ2 ≠
μ3
(b) Which of the following conditions satisfied must be satisfied
for using an ANOVA to analyze this data set? Select all that
apply.
DependenceIndependenceEqual standard deviationsNonequal standard
deviationsX is normally distributed for each groupX is
normally distributed for at least one of the groups
(c) What is the p-value of the ANOVA test? Use 4 decimal
places.
(d) If α = 0.05, what is your conclusion?
There is insufficient evidence at the α = 0.05 significance
level to conclude that the mean age of White Oaks differs at
between at least two sites.The data provides sufficient evidence at
the α = 0.05 significance level to conclude that the mean age of
White Oaks is the same for all three
sites. The data provides sufficient evidence
at the α = 0.05 significance level to conclude that the mean age of
White Oaks differs between at least two sites.
(e) What does the p-value tell us?
The probability we would find sample means at least as far apart
as we did, assuming the population means are all equal.The
probability the population means for all three groups are equal,
assuming the sample means are as given
above. The probability the population means
are different for at least one group, assuming the sample means are
as given above.The probability we would find sample means at least
as close together as they are, assuming the population means are
all equal.
(f) Suppose the mean age of White Oaks in the Lower peninsula were
200, the mean age of all White Oaks in the Upper peninsula were
300, and the mean age of all White Oaks in the Lower peninsula were
200. Based on your conclusion in the previous problem, you have
made.
--- I just need part e answered. Thanks so much.
Quercus alba, in the following three locations. Site 1 : Lower
peninsula, MI, near Lake Michigan Site 2 : Upper peninsula, MI,
near Lake Superior and Site 3 : Lower peninsula, MI, near Saginaw
Bay (are not all the same). To test this theory, you take 3 simple
random samples of 35 trees from each site, and record the ages of
each White Oak in each sample.
(a) What are the hypotheses?
H0: μ1 = μ2 =
μ3 vs. Ha: At least two of the means
differ from each other.H0: μ1 =
μ2 = μ3 vs. Ha: At least
two of the means are different from the
third. H0: μ1 =
μ2 = μ3 vs. Ha: At least
one of the means is different from all the others.H0:
μ1 = μ2 = μ3;
Ha: μ1 ≠ μ2 ≠
μ3
(b) Which of the following conditions satisfied must be satisfied
for using an ANOVA to analyze this data set? Select all that
apply.
DependenceIndependenceEqual standard deviationsNonequal standard
deviationsX is normally distributed for each groupX is
normally distributed for at least one of the groups
(c) What is the p-value of the ANOVA test? Use 4 decimal
places.
(d) If α = 0.05, what is your conclusion?
There is insufficient evidence at the α = 0.05 significance
level to conclude that the mean age of White Oaks differs at
between at least two sites.The data provides sufficient evidence at
the α = 0.05 significance level to conclude that the mean age of
White Oaks is the same for all three
sites. The data provides sufficient evidence
at the α = 0.05 significance level to conclude that the mean age of
White Oaks differs between at least two sites.
(e) What does the p-value tell us?
The probability we would find sample means at least as far apart
as we did, assuming the population means are all equal.The
probability the population means for all three groups are equal,
assuming the sample means are as given
above. The probability the population means
are different for at least one group, assuming the sample means are
as given above.The probability we would find sample means at least
as close together as they are, assuming the population means are
all equal.
(f) Suppose the mean age of White Oaks in the Lower peninsula were
200, the mean age of all White Oaks in the Upper peninsula were
300, and the mean age of all White Oaks in the Lower peninsula were
200. Based on your conclusion in the previous problem, you have
made.
--- I just need part e answered. Thanks so much.