Logging Activity in Forests Is Thought to Affect the Behavior $\mathrm { km } ^ { 2 }$

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 $\mathrm { km } ^ { 2 }$ ) 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 $20 \mathrm {~km} ^ { 2 }$ . 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 non-logged forests? Explain, using appropriate statistical terminology.