In a study designed to assess the impact that a fire as on deer behavior and hab
ID: 3150892 • Letter: I
Question
In a study designed to assess the impact that a fire as on deer behavior and habitat, forest ecologists established a 3000 acre study site, part of which had been affected by a major burn 6 months prior. The site was divided into 4 areas: The inner burn area, the inside edge, the outside edge, and the outer area (which had little to no actual fire damage). One of the study questions was whether or not deer showed a preference for one or more areas over the others. The specific acreage for each area is summarized in Table 1. Is there enough evidence to conclude that the deer in this habitat preferred one area over the other? During the course of the study observers recorded a total of 117 deer in the study area. 5 were seen in the inner burn area, 12 were seen in the inner edge area, 22 were seen in the outside edge area, and the rest were seen in the outer area. Let = 0.1.
A) Give the hypothesized distribution of the deer. That is, give the hypothesized proportion of deer for each of the four areas.
Hint: Since the acreage for each area is different, we'd expect to see more deer in the larger areas regardless of preference.
Round all answers to three decimal places.
Inner Burn Area:
Inside Edge:
Outside Edge:
Outer Area:
B) The number of degrees of freedom for this study is:
C) Fill in Table 2, which you will use to find the test statistic. The last column is (observed - expected)2/expected.
Note: Round to 3 decimal places where necessary.
D) What is the test statistic?
E) What is the critical value for this test?
F) Based on your critical value and conclusion, the corresponding decision/conclusion is:
Reject Ha and conclude that deer have no preference. FTR Ho and do not conclude that deer prefer one area over the others. FTR Ha and conclude that deer prefer one area over the others. Reject Ha and do not conclude that deer prefer one area over the others. Reject Ho and conclude that deer have no preference. Reject Ho and conclude that deer prefer one area over the others.
Table 1: Acreage Area Inner Burn Inside Edge Outside Edge Outer Acreage 520 210 240 2030Explanation / Answer
a) H0: deer prefer one area over the others
H1: deer have no prefer one area over the others
B) Degrees of freedom = 4-1 = 3df
c) The expected frequency is calculated as observed frequency * proportion
d) Test statistic: Chisquare value = 32.041
e) The critical value for this test = 7.815
f) Here Chisquare value > critical value, so we reject H0.
Thus, Reject Ho and conclude that deer have no preference.
Acreage Proportion Inner Burn Area: 520 0.173 =520/3000 Inside Edge: 210 0.07 =210/3000 Outside Edge 240 0.08 =240/3000 Outer Area 2030 0.677 =2030/3000 Total: 3000 1