W13 - HW Solutions

01

(a)

• Null Hypothesis : “The expected paper clip length is not inches”
• Alternative Hypothesis : “The expected paper clip length is inches”

Let be the length of the paperclips for our sample. For the sample, assume and . Thus, .

By symmetry, since we want a two-tailed test, it suffices to find the rejection region at one tail (we can then extrapolate for the second tail). We then have, for the lower rejection region:

Solving for , we have . By symmetry, the lower bound for our upper rejection region is . Thus, our rejection region is

By definition, .

---

(b) A Type-II error occurs when the Null Hypothesis is incorrectly accepted, when it is actually false.

Thus, .

Thus, now let . We then have:

02

03

The rejection region is . So if shipping takes 8 or 9 days, we will reject .

08

1
2
3
4
5

• If or the doctor should diagnose the patient as having the disease.
• If the doctor should not diagnose the patient as having the disease.

10

If

THEN put in .

Solve:

If , decide .

If , decide .