Logging activity in forests is thought to affect the behavior of black bears (Ur

Question

Logging activity in forests is thought to affect the behavior of black bears (Ursus americanus). An important measure of animal behavior is the home range, the area used by animals in their lives. In a study of black bears in a logged Canadian forest, the spring and early summer home range (in km2 ) of 12 radio-collared female black bears was measured with the following results: 39.9, 23.5, 42.1, 29.4, 34.4, 40.9, 27.9, 22.3, 13.0, 20.1, 13.3, 8.6 a) Construct and interpret a 95% confidence interval for the mean home range of female black bears in this logged forest. b) The typical home range of females in forests with no logging is 20 km2 . Based on the confidence interval from part (a), do you think that the mean home range size of females in this logged forest could be the same as the mean home range size in nonlogged forests? Explain, using appropriate statistical terminology.

Explanation / Answer

Solution:-

(a) Construct and interpret a 95% confidence interval for the mean home range of female black bears in this logged forest.

If (n < 30),

CI = x ± t/2 × (/n)

Where, x = Mean

= Standard Deviation

= 1 - (Confidence Level/100)

t/2 = t-table value

CI = Confidence Interval

using the given data - 39.9, 23.5, 42.1, 29.4, 34.4, 40.9, 27.9, 22.3, 13.0, 20.1, 13.3, 8.6

we have, n = 12, x = 26.2833, = 10.98 and = 0.05

C.I. for Mean = 20.609 < µ < 31.958

b) The typical home range of females in forests with no logging is 20 km2 . Based on the confidence interval from part (a), do you think that the mean home range size of females in this logged forest could be the same as the mean home range size in nonlogged forests? Explain, using appropriate statistical terminology.

Here, we are given that the typical home range of females in forests with no logging is 20 km2. This given mean lies between the confidence interval of the mean home range of female black bears in logged forest.

Thus, we can say that at 95% confidence interval the mean home range size of females in this logged forest could be the same as the mean home range size in nonlogged forests.

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