Question: (continuation) If the variance exceeds 2, there will be quality problems. Suppose that the manufacturer tests the hypotheses \[{{H}_{0}}:{{\sigma }^{2}}\le 2\] vs. \[{{H}_{1}}:{{\sigma }^{2}}>2\] and the rejection region is the set of all realizations \[{{x}_{1}},\ldots ,{{x}_{10}}\] for which the sample variance \[{{s}^{2}}>3.75977\] .

1. What is the significance level of the test?
2. What is the power of the test if \[{{\sigma }^{2}}=6\] ?
3. Suppose the realized measurements are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Is \[{{H}_{0}}:{{\sigma }^{2}}\le 2\] accepted or rejected? What is the p -value of the test?
4. Briefly discuss the issues (pros and cons) involved in interchanging the two hypotheses – i.e., for testing \[{{H}_{0}}:{{\sigma }^{2}}\ge 2\] vs. \[{{H}_{1}}:{{\sigma }^{2}}<2\] , instead of \[{{H}_{0}}:{{\sigma }^{2}}\le 2\] vs. \[{{H}_{1}}:{{\sigma }^{2}}>2\] . [You are not required to do the interchanged test - just discuss it .]

Price: $2.99

Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document