Question

A random sample is obtained from a population with μ = 120 and σ = 20, and a treatment is administered to the sample. Which of the following outcomes would be considered noticeably different from a typical sample that did not receive the treatment?

a. n = 36 with M = 121

b. n = 36 with M = 123

c. n = 144 with M = 121

d. n = 144 with M = 124

Answer 1

Solution:

          we are given that : a random sample is obtained from a population with μ = 120 and σ = 20, and a treatment is administered to the sample.

         We have to find from the following outcomes that would be considered noticeably different from a typical sample that did not receive the treatment.

a. n = 36 with M = 121

b. n = 36 with M = 123

c. n = 144 with M = 121

d. n = 144 with M = 124

Thus we need to find z score for each :

z score formula :

$z = \frac{M-\mu}{\sigma /\sqrt{n}}$

Part a)

n = 36 with M = 121

$z = \frac{M-\mu}{\sigma /\sqrt{n}}$

$z=\frac{121-120}{20/\sqrt{36}}$

$z=\frac{1}{20/6}$

$z=\frac{1}{3.333333}$

$z=0.30$

b) n = 36 and M = 123

$z=\frac{123-120}{20/\sqrt{36}}$

$z=\frac{3}{20/6}$

$z=\frac{3}{3.333333}$

$z=0.90$

c) n = 144 and M = 121

$z=\frac{121-120}{20/\sqrt{144}}$

$z=\frac{1}{20/12}$

$z=\frac{1}{1.666667}$

$z=0.60$

d)   n = 144 and M = 124

$z=\frac{124-120}{20/\sqrt{144}}$

$z=\frac{4}{20/12}$

$z=\frac{4}{1.666667}$

$z=2.40$

Thus z = 2.40 is for n = 144 with M = 124,

thus outcome d. n = 144 with M = 124 would be considered noticeably different from a typical sample that did not receive the treatment.