The value of the z-score that is obtained for a hypothesis test is influenced by several factors. Some factors influence the size of the numerator of the z-score and other factors influence the size of the standard error in the denominator.

Question

For each of the following indicate whether the factor influences the numerator or denominator of the z-score and determine whether the effect would be to increase the value of z(farther from zero) or decrease the value of z (closer to zero).

In each case, assume that all other components of the z-score remain constant.

a)increase the sample size
b) increase the population standard deviation
c)increase the difference between the sample mean and the value of µ specified in the null hypothesis

Answer 1

Z = (mean - ƒÊ)/SE

Anything that increases the numerator, increases the value of Z. Anything that increases the value of the denominator, decreases the value of Z.

a) since a larger sample would decrease the SE, that would increase Z.

b) since the increase in population SD would increase the SE, it would decrease Z.

c) since the difference is in the numerator, it would increase Z.

I hope this helps. Thanks for asking.