Question

1. A sample of n=18 individuals is selected from a population with a mean of µ=77, and a treatment is administered to the individuals in the sample. A treatment is administered to the individuals in the sample and after treatment, the sample variance is found to be s²=144.
   a. If the treatment has a 3-point effect and produces a sample mean of M=80, is this sufficient to conclude that there is a significant treatment effect effect using a two-tailed test with a α=.05? Be sure to show all formulas with symbols (and plug in numbers), steps, processes and calculations for all parts of the answers.
   b. If the treatment has a 7-point effect and produces a sample mean of M=84, is this sufficient to conclude that there is a significant treatment effect using a two-tailed test with a α=.05? Be sure to show all formulas with symbols (and plug in numbers), steps, processes and calculations for all parts of all answers.

Answer 1

a) H0: There is no significant treatment effect effect using a two-tailed test with a α=.05

H1: There is significant treatment effect effect using a two-tailed test with a α=.05

i.e.

Thus we conclude that  there is no significant treatment effect effect using a two-tailed test with a α=.05

b)

H0: There is no significant treatment effect effect using a two-tailed test with a α=.05

H1: There is significant treatment effect effect using a two-tailed test with a α=.05

i.e.

Thus we conclude that there is significant treatment effect effect using a two-tailed test with a α=.05