Question

A sample of n = 16 individuals is selected from a population with µ = 30. After a treatment is administered to the individuals, the sample mean is found to be M = 33. a. If the sample variance is s2 = 16, then calculate the estimated standard error and determine whether the sample is sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05. b. If the sample variance is s2 = 64, then calculate the estimated standard error and determine whether the sample is sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05. c. Describe how increasing variance affects the standard error and the likelihood of rejecting the null hypothesis

Answer 1

a)

from above estimated standard error =3.00

as test statistic falls in rejection region, we reject null and conclude that there is sufficient evidence that the treatment has a significant effect.

b)

standard error =2.00

as test statistic does not falls in rejection region, we do not reject null and can not conclude that the treatment has a significant effect.

c)

increasing variance increase standard error and likelihood of rejecting the null hypothesis decreases,