LounchPad Online Resources The StatBoards video, Matched Pairs t Procedures, discusses examples of inference for matched pairs Apply Your Knowledge Many exercises from this point on ask yone to give the P-value of a t test. If you have suitable recmology, give the exact P-value. Otherwise, use Table C to give two P lies exact P-vaue. Otherwise, use Table C to give two values between which 20.11 Eye Grease. grease under their eyes to reduce glare. Does eye grease lo student subjects took a test of sensitivity to contrast after three hours facing into bright sun, both with and without eye grease. (Greater sensitiv- ity to contrast improves vision and glare reduces sensitivity to contrast.) This is a matched pairs design. Here are the differences in sensitivity, with eye grease minus without eye grease : 10 am EYEGRS Athletes performing in bright sunlight often smear black eye ase work? In one study reduce glare. Does eye gre eye grease minus without eye grease:1 IEYEGRS 07 0.64 -0 0.12 0.05 -0.18 0.14 -0.16 0.03 0.05 0.02 0.430.24-0.11 0.280.05 0.29 We want to know whether eye grease increases sensitivity to contrast on the average. Do the data support this idea? Complete the Plan, Solve, and Con- clude steps of the four-step process, following the model of Example 20.4 12 Eye Grease, Continued. How much more sensitive to contrast are ease than without eye grease? Give a 99% confidence ur
Let
ud = u(with grease) - u(without grease)
Formulating the null and alternative hypotheses,
Ho: ud <= 0
Ha: ud > 0
As we can see, this is a right tailed test.
Thus, getting the critical t,
df = n - 1 = 15
tcrit = + 1.753050356
Getting the test statistic, as
X = sample mean = 0.10125
uo = hypothesized mean = 0
n = sample size = 16
s = standard deviation = 0.226329406
Thus, t = (X - uo) * sqrt(n) / s = 1.789427221
Comparing |t| > 1.753, we REJECT THE NULL HYPOTHESIS.
Thus, there is significant evidence that eye grease increases eye sensitivity to contrast. [CONCLUSION]
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