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 changed 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

1. Calculate the sample mean and sample standard deviation for the differences.

2. Calculate the margin of error, E for a 95% confidence interval for the population difference.

3. c. Calculate the 95% confidence interval for the population difference, based on this sample.

   d. Explain, to a non-Statistics person, what the confidence interval means, including whether or not we can conclude that there is a difference in home ranges for all deer in this area during those two years.

Answer 1