The types of browse favored by deer are shown in the followi

The types of browse favored by deer are shown in the following table. Using binoculars, volunteers observed the feeding habits of a random sample of 320 deer. Plant Composition Observed Number of Deer: We want to test the claim that the natural distribution of browse fits the deer feeding pattern using a 5% level of significance, State the null and alternate hypotheses. 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.) What is the degree of freedom? Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) Based on your answers in parts (a) to (c). will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories? Explain how you made your decision.

Solution

a)

Ho: The natural distirbution of browse fits the deer feeding pattern.

H1: The natural distirbution of browse does not fit the deer feeding pattern.

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b)

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
93   102.4   0.862890625  
135   123.84   1.005697674  
40   38.4   0.066666667  
32   29.76   0.168602151  
20   30.4   3.557894737  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    5.661751853   [ANSWER, CHI-SQUARE STATISTIC]

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As df = a - 1,           
          
a =    5      
df = a - 1 =    4   [ANSWER, DEGREES OF FREEDOM]

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c)  

Also, the p value is, using technology,          
          
p =    0.225872986   [ANSWER, P VALUE]

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d)  
          
As P > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.