9/16/2014
Researchers
studied the behavior of birds that were searching for seeds and
insects in an Oregon forest. In this forest, 54% of the trees were
Douglas firs, 40% were ponderosa pines, and 6% were other types of
trees. At a randomly selected time during the day, the researchers
observed 156 red-breasted nuthatches: 70 were seen in Douglas firs,
79 in ponderosa pines, and 7 in other types of trees. Do these data
suggest that nuthatches prefer particular types of trees when they’re
searching for seeds and insects?
a) Which Chi-Square Test would
you perform to answer this question?
b) State
the Null and Alternative Hypothesis in context.
c) Tabulate the
Observed and Expected frequencies, and calculate the P-value.
d)
Write a brief conclusion to answer the question in the problem.
Scroll down for the solution.
9/16/2014
Solution.
a)
Chi-Square
Goodness of Fit Test.
b)
Ho: Nuthatches don't prefer particular types of trees when they’re
searching for seeds and insects or
The
distribution of trees that nuthatches use for searching for seeds and
insects conforms to the model of Pd = 54%, Pp = 40%, Po = 6% or
The
model of Pd = 54%, Pp = 40%, Po = 6% is valid
H1: Ho: Nuthatches
prefer certain types of trees when they’re searching for seeds
and insects or
The
distribution of trees that nuthatches use for searching for seeds and
insects does not
conform
to the model of Pd = 54%, Pp = 40%, Po = 6% or
The
model of Pd = 54%, Pp = 40%, Po = 6% is not
valid
c)
|
O |
E |
D |
70 |
84.2 |
PP |
79 |
62.4 |
O |
7 |
9.4 |
X2(2
df)
= 7.4182
→ P-value,
P = P(X2
>
7.4182) = 0.0245
d) Reject Ho → Nuthatches prefer particular
types of trees when they’re searching for seeds and insects.