A camera has been developed to detect the presence of cataract more accurately.

Question

A camera has been developed to detect the presence of cataract more accurately. Using this camera, the gra level of each point (or pixel) in the lens of a human eye can be characterized into 256 gradation, where a gray level of 1 represents black and a gray level of 256 represents white. To test the camera, photographs were taken of 6 randomly selected normal eyes and 6 randomly selected cataractous eyes (the two groups consist of different people). The median gray level of each eye was computed over the 10,000+ pixels in the lens. The data are given in table 8.14.

QUESTION: Please write a null hypothesis and alternative hypothesis in sentence format based on the information given above and based on the following question.

8.28 What statistical procedure can be used to test whether there is a significant difference in the median gray levels between cataractous and normal eyes? (DO NOT SOLVE THIS) I just need the null and alternative hypothesis in words to interpret my answer.**

Explanation / Answer

Solution:-

We can use two sample t-test.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: Normal = Cataractous , There is no mean difference in the median gray levels between cataractous and normal eyes.

Alternative hypothesis: Normal Cataractous , There is mean difference in the median gray levels between cataractous and normal eyes.

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.

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