The types of browse favored by deer are shown in the followingtable. Using binoculars, volunteers observed the feeding habits ofa random sample of 320 deer.

Type of Browse	Plant Composition in Study Area	Observed Number of Deer Feeding on This Plant
Sage brush	32%	105
Rabbit brush	38.7%	125
Salt brush	12%	46
Service berry	9.3%	22
Other	8%	22

Use a 5% level of significance to test the claim that thenatural distribution of browse fits the deer feeding pattern.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: The distributions are different.
H₁: The distributions are the same.

H₀: The distributions are the same.
H₁: The distributions are thesame.    

H₀: The distributions are the same.
H₁: The distributions are different.

H₀: The distributions are different.
H₁: The distributions are different.

(b) Find the value of the chi-square statistic for the sample.(Round the expected frequencies to at least three decimal places.Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

Yes

No    

What sampling distribution will you use?

binomial

Student's t    

uniform

normal

chi-square

What are the degrees of freedom?


(c) Estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value <0.100    

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis that the population fits thespecified distribution of categories?

Since the P-value > ?, we fail to rejectthe null hypothesis.

Since the P-value > ?, we reject the nullhypothesis.    

Since the P-value ? ?, we reject the nullhypothesis.

Since the P-value ? ?, we fail to reject thenull hypothesis.

(e) Interpret your conclusion in the context of theapplication.

At the 5% level of significance, the evidence is sufficient toconclude that the natural distribution of browse does not fit thefeeding pattern.

At the 5% level of significance, the evidence is insufficient toconclude that the natural distribution of browse does not fit thefeeding pattern.