Asample is selected from a population with μ = 50, and a treatment is administered to the sample. if the sample variance is s2 = 121, which set of sample characteristics has the greatest likelihood of rejecting the null hypothesis?
a. m = 49 for a sample size of n = 75
b. m = 49 for a sample size of n = 15
c. m = 45 for a sample size of n = 15
d. m = 45 for a sample size of n = 75

The sample d. M = 45 for a sample size of n = 75  has the greatest likelihood of rejecting the null hypothesis.

Step-by-step explanation:

Greatest likelihood of rejecting the null hypothesis can be found by calculating the z-cores of the sample means. The sample with the biggest absolute z-score value has grater likelihood of rejecting the null hypothesis.

Z-score of the sample means can be calculated as follows:

z= where

a. M = 49 for a sample size of n = 75

Then z(a)= ≈ −0.787

b. M = 49 for a sample size of n = 15

z(b)= ≈ −0.352

c. M = 45 for a sample size of n = 15

z(c)= ≈ −1.760

d. M = 45 for a sample size of n = 75

z(d)= ≈ −3,936

Since z(d) is the lowest, it has the biggest absolute z-value. Therefore sample d is more likely to reject the null hypothesis.

answer: can and shows the work

step-by-step explanation: