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) = 7.4182P-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.