1. The value of the z-score that is obtained for a hypothesis test is influence by several factors. Some factors influence the size of the numerator of the z-score and the factors influence of the standard error in the denominator. For 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 component of the z-score remain constant.
2. Briefly explain the advantage of using an alpha level of .01 versus of .05. In general, what is the disadvantage of using a smaller alpha level?
3. A sample of n=9 scores is obtained from a normal population distribution with σ = 12 the sample M =60
a. With a two-tailed test and a= 0.5 use the sample data to test the hypothesis and the population mean is µ =65
b. With a two- tailed test and a =.05 use the sample data to test the hypothesis that the population is µ =55
c. In parts (a) and (b) of this problem, you should find that µ=65 and µ =55 are both acceptable hypotheses. Explain how two different values can both be acceptable.
The solution describes the nature of Z statistic in the following cases
a. Increase the sample size
b. Increase the population standard deviation and
c. Increase the difference between the sample mean and the value of the µ specified in the null hypothesis.