Question

A sample is obtained from a population with u=40 and o=6. Which of the following sample would produce the z scores closest to 0?

a) a sample (n=36) with M=43

b) a sample (n=64) with M=42

c) a sample (n=100) with M=38

d) a sample (n=16) with M=37

Answer 1

Test statistic = z

= (M - ) /   / n

(a)

z score

= (43 - 40) / 6 / 36

= 3

(b)

z score

= (42 - 40) / 6 / 64

= 2.67

(c)

z score

= (38 - 40) / 6 / 100

= -10

(d)

z score

= (37 - 40) / 6 / 16

= -2

sample d) a sample (n=16) with M=37 is closest to 0