What is the null and alternative hypotheses?

Question

An SRS of 16 student subjects took a sensitivity to contrast after 3 hours facing into bright sun, both with and without eye grease. This is a matched pairs design. Here are the differences in sensitivity, with eye grease minus without eye grease: 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     We want to know whether eye grease increases sensitivity on the average.  What are the null and alternative hypotheses?  What does the parameter µ in the hypotheses concern?  What is the value of the test statistic?  Assume that the differences in sensitivity follow a normal distribution in this population with the standard deviation of σ = 0.22. Give answer to 2 decimal places.  What is the p-value of the test?  Give answer to 3 decimal places.   What is your conclusion?

Answer 1

Vivian,

 

μ=difference in sensitivity of each of the 16 students.

 

H₀:μ≤0 no increase or a decrease

H_a:μ>0 an increase

 

Test statistic is Z=(μ-0)/σ

 

Can you finish the rest of the problem? You have to calculate the mean of the sample.

 

Jim

Answer 2

H_{0 :} Null hypothesis is : Eye grease increases sensitivity on the average 

H _A: Alternative hypothesis : Eye grease does not increase sensitivity.