Chapter 11.1, Problem 14E

a)

To determine

To perform chi-square goodness of fit test.

Answer to Problem 14E

There is sufficient evidence to support the claim that seagulls show a preference for where they land.

Explanation of Solution

Given:

Observed count	Frequency
128	56%
61	29%
11	15%

Calculation:

The null and alternative hypotheses:

  $H_0:p_1=0.56,p_2=0.29,p_3=0.15$

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

Using excel,

Observed	expected	O - E	(O - E)² / E	% of chisq
128	112.000	16.000	2.286	15.79
61	58.000	3.000	0.155	1.07
11	30.000	-19.000	12.033	83.14
Total=200	200.000	0.000	14.474	100.00
14.47	chi-square
2	df
.0007	p-value

Decision: P-value < 0.05, reject H0.

Conclusion: There is sufficient evidence to support the claim that seagulls show a preference for where they land.

b)

To determine

To explain which type of ground, do the seagulls preferred the most and least by using relative proportion.

Answer to Problem 14E

Most preferred ground is sand and least preferred is rocks.

Explanation of Solution

Given:

Type	Observed count	Frequency
sand	128	56%
mud	61	29%
rocks	11	15%
Total	200	100%

Calculation:

As per relative proportion, most preferred ground is sand and least preferred is rocks.