Chapter 11.1, Problem 13E

a)

To determine

To perform chi-square goodness of fit test.

Answer to Problem 13E

There is sufficient evidence to support the claim that nuthatches prefer particular types of trees.

Explanation of Solution

Given:

Count	Frequency
70	0.54
79	0.4
7	0.06

Calculation:

The null and alternative hypotheses:

  $H_0:p_1=0.54,p_2=0.4,p_3=0.06$

  $H_a:Atleastoneofthe{p}_i’sisincorrect.$

Using excel,

	observed	expected	O - E	(O - E)² / E	% of chisq
	70	84.240	-14.240	2.407	32.45
	79	62.400	16.600	4.416	59.53
	7	9.360	-2.360	0.595	8.02
Total	156	156.000	0.000	7.418	100.00
	7.42	chi-square
	2	Df
	.0245	p-value

Decision: P-value < 0.05, reject H0.

Conclusion: There is sufficient evidence to support the claim that nuthatches prefer particular types of trees.

b)

To determine

To explain which type of nuthatches preferred the most by using relative proportion.

Answer to Problem 13E

The most preferred nuthatches as its proportion is higher. The least preferred is other types of trees as its proportion is very less.

Explanation of Solution

Given:

Count	Frequency
70	0.54
79	0.4
7	0.06

Calculation:

As per relative proportion, Douglas firs seems to be most preferred nuthatches as its proportion is higher. The least preferred is other types of trees as its proportion is very less.