The value of the z-score that is obtained for a hypothesis test is influenced by

Question

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. 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). For the aforementioned, be sure to discuss why the factors influence the z-scores and why the values increase or decrease. 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 the population mean specified in the null hypothesis.

Explanation / Answer

Answer:

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. 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). For the aforementioned, be sure to discuss why the factors influence the z-scores and why the values increase or decrease. In each case, assume that all other components of the z-score remain constant.
a. Increase the sample size.
z score will increase. Increase the sample size will decrease the standard error. This factor influences the denominator. Since the denominator decreases, z score increases.

b. Increase the population standard deviation.

z score will decrease. Increase the population standard deviation will increase the standard error. This factor influences the denominator. Since the denominator increases, z score decreases.

c. Increase the difference between the sample mean and the value of the population mean specified in the null hypothesis.

z score will increase. Increase in the difference between the sample mean and the value of the population mean will increase the value of the numerator. Since the numerator increases, z score increases.

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