**Examining the Effectiveness of Eye Grease in Bright Sunlight**Athletes performing in bright sunlight often apply black eye grease under their eyes to reduce glare. Does eye grease work? In one study, 16 student subjects took a test of visual sensitivity to light-and-dark contrast after three hours facing bright sun, both with and without eye grease. This is a matched pairs design. If eye grease is effective, subjects will be more sensitive to contrast when they use eye grease. The differences in sensitivity, with eye grease minus without eye grease, are provided in the table below.**Differences in Sensitivity**| 0.07 | 0.64 | -0.12 | -0.05 | -0.18 | 0.14 | -0.16 | 0.03 ||------|------|-------|-------|-------|------|-------|------|| 0.05 | 0.02 | 0.43 | 0.24 | -0.11 | 0.28 | 0.05 | 0.29 |To access the data, click the link for your preferred software format: CSV | Excel (xls) | Excel (xlsx) | JMP | Mac-Text | Minitab14-18 | Minitab18+ | PC-Text | R | SPSS | TI | CrunchIt! **State:** We want to know whether eye grease increases sensitivity on average.Data simulated from a Normal distribution based on information in Brian M. DeBroff and Patricia J. Pahk, "The ability of periorbitally applied antiglare products to improve contrast sensitivity in conditions of sunlight exposure," *Archives of Ophthalmology*, 121 (2003), pp. 997–1001. **Text Transcription for Educational Website:**---Suppose that the subjects are an SRS of all young people with normal vision, that contrast differences follow a Normal distribution in this population, and that the standard deviation of differences is σ = 0.22. Carry out a test of significance.**SOLVE: What is the value of the test statistic? Give your answer to two decimal places.**z = [Blank Space]**Find the P-value of the test. Give your answer to four decimal places.**P-value: [Blank Space]© Macmillan Learning---**Explanation:**This text is part of a statistical problem involving hypothesis testing. The task involves finding the value of a test statistic (z-score) to assess if there is a significant difference in contrast sensitivity in conditions outlined. The problem assumes a simple random sample (SRS) from a population of young individuals with normal vision. The known standard deviation for the differences is 0.22. The second part of the problem requires calculating the P-value, which will help in deciding the significance of the test. The answers should be presented with specific decimal precision as instructed.

In study 16 students subject take to test of sentivity to contrast after 3 hour facing into bright sun both, withand without eye grace.We want to know wether the eye grease has a significant impact on eye sensitivitygiven that :sample size = 16standard deviation of differences =0.22SRS of all young people with normal vision that contrast difference follow normal distribution..to find value of test statistics.p-value of the test the data are 0.070.64-0.12-0.05-0.180.14-0.160.030.050.020.430.24-0.110.280.050.29the t- test to use find the eye grease has a significant impact on eye sesitivityThe test hypothesis are null hypothesis Vs alternative hypothesis test statistics isThe test statistics value is 1.84Formula for p-value is p-value=P( t >) =2*(1-P( t <184)) = 0.0856where t follows student's t distribution with (n-1) degree of freedomconsider apha =0.05calculate above probability using excelconclusion:P value is greter than alpha valkue the we fail to reject null hypothesis.p-value(0.0856) > alpha(0.05)then we fail to reject null hypothesis.The eye grases has a significant imapact on eye sesitivityThe test statistic value is 1.84The p-value is 0.0856The Eye grease have a significant impact on eye sesitivity