The following data is sampled from an exponential population with unknown parameter β.
|
6.99
|
2.84
|
0.41
|
3.75
|
2.16
|
|
0.52
|
0.67
|
2.72
|
5.22
|
16.65
|
|
10.36
|
1.66
|
3.26
|
1.78
|
1.31
|
|
5.75
|
0.12
|
6.51
|
4.05
|
1.52
|
(i) On the basis of the exact sampling distribution of the sample mean, X¯, determine a 95% con?dence interval estimate of the population parameter, β.
(ii) Test the hypothesis H0: β = 4 versus the alternative H0: β /= 4. What is the p-value associated with this test?
(iii) Repeat the test in (ii) using the normal approximation (which is not necessarily valid in this case). Compare this test result with the one in (ii).