A camera has been developed to detect the presence of cataract more accurately. Using this camera, the gray level of each point (or pixel) in the lens of a human eye can be characterized into 256 gradations, 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. Of note, the two study groups consist of eyes from different people. The median gray level of each eye was computed over the 10,000+ pixels in the lens.

Eye number	Cataractous median gray level	Normal median gray level
1	161	158
2	140	182
3	136	185
4	171	145
5	106	167
6	149	177

We want to test whether there is a significant difference in the median gray levels between cataractous and normal eyes. We analyze the data using SAS's TTEST procedure and observe the results shown in Table. Based on those findings, answer the following questions.

1) Report and interpret the 95% confidence interval of the mean of median gray level in Normal group. [Report two decimal places]

2) Identify the dependent variable and the independent or explanatory variable(s) in this study. Also, state the Null and Alternative hypotheses.

3) An important step in an Independent t-Test is to first test for equal variance. Based on the information in the "Equality of Variances" portion of the output table, what is your decision about the Null hypothesis regarding equal variances (i.e. H0: Variance1 = Variance2)? In your answer, report the test statistic and P-value from the SAS output that you used to make your decision.

4) Now we want to test the Null hypothesis that was stated in Question 2. From the "T-Tests" portion of the output, report the test statistic, degrees of freedom (DF), and P-value that should be used to test the Null hypothesis. Based on that information, what conclusion can you make about the Null hypothesis (i.e. Reject or Fail to Reject the Null)?

5) Interpret these findings (3-4 sentences max). Your answer should (1) restate the findings, and (2) note the generalizability of these results.