1. (1.3627, 3.0373)
2. a. (-0.01109, 0.09309)
b. No, we have no evidence against the claim. Zero is in the confidence interval − it is believable that there is no difference between the means.
d. With no difference between the underlying means, a difference in the sample means at least as large as the difference observed here would occur 12.28% of the time. A small probability, say ≤ 5% would indicate such a rare occurrence that it would not be believable that the two underlying means were equal. Here, the probability of 0.1228 is large enough for us to believe that there is no difference between the two underlying means.
3. a. (3.667, 7.733)
b. The samples should be large, normal and independent.
c. Yes, because 0 is not included in the confidence interval.