Question

1. For each of the following three statements:

(1) identify the most suitable statistical test based on the problem described

(2) declare the hypotheses of the chosen test, based on the statement (in words or in mathematical language)

(3) establish the statistical decision rule for the chosen test, including the critical value.

(9 points)

(a) Ophthalmologists want to compare the visual acuity of people who have had corrective laser surgery (7 individuals) and those who have not had surgery (10 individuals). Visual acuity is measured as the maximum distance (in m) at which characters can be discerned. The acuity is distributed normally and its variance is homogeneous between the groups.

(b) Ophthalmologists want to compare the visual acuity of people who have had corrective laser surgery (7 individuals) and those who have not had surgery (10 individuals). Visual acuity is measured on a semi-quantitative scale ranging from 0 (poor) to 10 (perfect)

c) Ophthalmologists want to compare the visual acuity of the right eye and the left eye of a group of 10 people. Visual acuity is measured as the maximum distance (in m) at which characters can be discerned. The acuity is distributed normally and its variance is homogeneous between the two eyes

Answer 1

Let's say ophthalmologist measures the average visual acuity for both samples. Then we need to test that there is difference in the average both of both the sample i.e they are not same.

Null hypothesis would be Ho: average visual acuity is same for both groups.

Alternative :

t test for the difference of means would be used as samples are small.

decision rule is mentioned above in the image in the last two lines.

if t calculated < t tabulated @ significance level 0.05 for n1+n2-2 degrees of freedom we accept otherwise we reject.

C) for this part as both eyes are of the same person so they are dependent.

and as sample is small and normal we used paired -t test for difference of means

calculate d=x-y

for all observations and then calculate

use this t-statistic for testing.

null hypothesis Ho; there is no significant difference between visual acuity of right and left eye.

alternative; (r-right and l-left)

you can take same 0.05 significance.

b) This part is slightly confusing . the best I can say for this is that we can use Mann -Whitney wilcoxon U -test (Non parametric) doesn't need any distribution assumptions.

right now I have this much information for this part ... i will be updating my answer soon for this part.

Thanks