4. Hypothesis Test 3
Glaucoma is a leading cause of blindness in the United States. N. Ehlers measured the corneal thickness of eight randomly selected patients who had glaucoma in one eye but not in the other. The results of the study were published as the paper ‐On Corneal Thickness and Intraocular Pressure, II" (Acta Ophthalmologica, Vol. 48, pp. 1107–1112).
The data on corneal thickness, in microns, are shown in the following table.
Patient | Normal | Glaucoma
1 | 484 | 488
2 | 478 | 478
3 | 492 | 480
4 | 444 | 426
5 | 436 | 440
6 | 398 | 410
7 | 464 | 458
8 | 476 | 460
We wish to perform a hypothesis test on the statement that mean corneal thickness is greater in normal eyes than in eyes with glaucoma, using a 10% significant level.
Answer the following questions.
a) Identify the two populations.
b) Which is the most appropriate test: non-pooled, pooled, or paired two-sample test?
c) State the null and alternative hypotheses.
d) Compute the value of the test statistics.
e) Find the p-value and state your decision, in context.