Question

The home range of an animal is the average area it occupies while foraging for food and defending its territory. It is thought that home ranges of animals usually do not change, except when an area is under environmental stress.  As part of a study of white-tailed deer in Florida, the deer were fitted with radio collars and their movements were followed over the course of a year.  The home range data are shown below, where the range is expressed in hectares (1 hectare  = 2.471 acres). The investigators are interested in determining whether the home ranges of white-tailed deer decreased over the course of a year.  

Radio-Collar ID #	1991 Home Range	1992 Home Range	Difference of Home Ranges (1992-1991)
1	80	175	95
2	268	206	−62
3	113	103	−10
4	83	93	10
5	24	9	−15
6	111	115	4
7	100	135	35
8	103	14	−89
9	293	104	−189
10	95	104	9
11	152	319	167
12	133	59	−74
13	293	125	−168
14	32	112	80
15	80	206	126
16	61	115	54
17	271	49	−222
18	111	150	39

Assume the conditions for normality and simple random samples are met.  Conduct a hypothesis test on the mean of the differences to determine if the home range for the deer has decreased due to human expansion into their habitat, using a 5% level of significance.

Answer 1

	sample 1	sample 2	Di	(Di - Dbar)²
sum =	2403	2193	210.000	193394.000

mean of difference ,    D̅ =ΣDi / n =   11.6667
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    106.6589

Ho :   µd=   0                  
Ha :   µd >   0                  
                          
Level of Significance ,    α =    0.05       claim:µd=0          
                          
sample size ,    n =    18                  
                          
mean of sample 1,    x̅1=   133.500                  
                          
mean of sample 2,    x̅2=   121.833                  
                          
mean of difference ,    D̅ =ΣDi / n =   11.667                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    106.6589                  
                          
std error , SE = Sd / √n =    106.6589   / √   18   =   25.1397      
                          
t-statistic = (D̅ - µd)/SE = (   11.66666667   -   0   ) /    25.1397   =   0.464
                          
Degree of freedom, DF=   n - 1 =    17                  
  
                          
p-value =        0.324242   [excel function: =t.dist.rt(t-stat,df) ]            
Conclusion:     p-value>α , Do not reject null hypothesis              

It can be concluded that home range for the deer has not been decreased due to human expansion into their habitat.

THANKS

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