Question

Hi,

I just need information about the way to start my exercice. I am not so sure...

So this exercice is below and here's what I want to do:

calculate both mean and both std for the two categories, then test H0 m1 = m2 and HA mi ≠ m2, calculate the t statistic and then a bilateral test ??

EXERCISE:

A team of researchers has designed a camera to detect, more accurately, the presence of a cataract in the eye. With the aid of the camera, the gray level of the lens of the eye is determined on a scale of 256 gradations. The presence of a cataract is characterized by a lower gray level value.
To evaluate the effectiveness of the camera, we take the photograph of an eye with crystalline healthy in 12 people and an eye presenting a cataract in 10 other people. For each eye, the gray level is determined. From the data obtained, test the null hypothesis that the camera does not distinguish the eyes with a healthy lens from those who present a cataract against the alternative hypothesis that the camera differentiates groups.
Make the table that allows you to obtain average ranks by assigning rank 1 to the smallest gray level value. Next, calculate R1, the sum of the ranks of the "healthy crystalline" group, then use the appropriate non-parametric test for this situation using the following values ​​already calculated: E (R1) = 138 and V (R1) = 229.2.

n1 <- c(158,182,185,145,167,177,200,165,185,194,154,162) crystalline healthy
n2 <- c(161,145,136,158,106,149,125,134,120,145) cataract

Answer 1

Here pvalue is 0.0001<0.05 hence we reject null hypothesis.

It-Test: Two-Sample Assuming Urzqual Variances cataract 137.9000 298.3222 17.2720 10.0000 Mean Variance Standard deviation Observations Hypothesized Mean Difference df test Statistic P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail crystaline Healthy 172.8333 285.9697 16.9106 12.0000 0.0000 19.0000 4.7687 0.0001 1.7291 0.0001 2.0930