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	PlantComposition in Study Area	Observed Number ofDeer Feeding on This Plant
Sage brush	          32%	96               Â
Rabbit brush	          38.7%	131               Â
Salt brush	          12%	40               Â
Service berry	            9.3%	25               Â
Other	            8%	28               Â

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 thesame.H₀: The distributions are the same.
H₁: The distributions aredifferent.    H₀: Thedistributions are the same.
H₁: The distributions are thesame.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?

YesNo    

What sampling distribution will you use?

chi-squareStudent'st    normalbinomialuniform

What are the degrees of freedom?


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

P-value > 0.1000.050 < P-value <0.100    0.025 < P-value <0.0500.010 < P-value < 0.0250.005 <P-value < 0.010P-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 > α, we fail to rejectthe null hypothesis.Since the P-value > α, wereject the null hypothesis.    Since theP-value ≤ α, we reject the null hypothesis.Sincethe P-value ≤ α, we fail to reject the nullhypothesis.

(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 isinsufficient to conclude that the natural distribution of browsedoes not fit the feeding pattern.