A sample 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 = 75b. M = 49 for a sample size of n = 15c. M = 45 for a sample size of n = 15d. M = 45 for a sample size of n = 75

Answer: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=[tex]\frac{M-mu}{\frac{s}{\sqrt{N} } }[/tex] where M is the sample meanμ=mu is the population means is the standard deviation (square root of variance)N is the sample size.a. M = 49 for a sample size of n = 75Then z(a)=[tex]\frac{49-50}{\frac{\sqrt{121}}{\sqrt{75} } }[/tex] ≈ −0.787b. M = 49 for a sample size of n = 15z(b)=[tex]\frac{49-50}{\frac{\sqrt{121}}{\sqrt{15} } }[/tex] ≈ −0.352c. M = 45 for a sample size of n = 15z(c)=[tex]\frac{45-50}{\frac{\sqrt{121}}{\sqrt{15} } }[/tex] ≈ −1.760d. M = 45 for a sample size of n = 75z(d)=[tex]\frac{45-50}{\frac{\sqrt{121}}{\sqrt{75} } }[/tex] ≈ −3,936Since z(d) is the lowest, it has the biggest absolute z-value. Therefore sample d is more likely to reject the null hypothesis.