**Mathematics: Sampling Statistics**

a)** Using a tail of one;**

Power = 1.0000

Df = 73

Critical t = -1.665

Non Centrality Parameter = 5.000

b)** Using a tail of one;**

Power = 0.9999

Df = 525

Critical t = -1.6478

Non Centrality Parameter = 2.3072

c) With a power of 90, an effect size of 0.4 and a confidence interval of 95%, the sample size will be 764.

d) Some of the 15 demographic characteristics I might hope CNN, Fox News etc to consider when they conduct telephone interviews on various topics for news programs include location, employment status, education, mobility, disability, income, home ownership, size of the family, marital status, generation (i.e. generation X, baby boomer generation etc.), social class, religion, ethnicity, nationality, occupation, the lifecycle of the family etc.

4) The scenario recounted herein involves the determination of a satisfaction survey of employee pay. I have a single week to get as many replies as possible as the end of the years as fast approaching and hence my boss must come up with a decision on whether to increase the pay or leave it as it is. My boss’ decision will be informed by my findings. My organization has 4,085 people and hence with that in mind, it is clear that the population is fairly large and hence gathering data from each constituent will not be workable.

For this case, I will use sampling which Fuller (2009) describes as the deliberate limiting of the study’s cases. It is important to note herein that while the issue at hand i.e. the determination of a satisfaction survey of employee pay is important and the participation of each and every individual would have been desirable but for practical reasons, sampling will be highly appropriate.

For this scenario, I will use non-random sampling. According to Levin et al. (2000), this procedure does not in any way allow all the cases the same probability of being included in the sample. The study’s context in this case will in one way or the other give me discretion when it comes to selecting a given sampling method or the criteria I will use to carry out the sampling.

The criterion I will use in the sample selection will primarily be the people’s willingness to participate. I select this criterion because in my view, it is not in any way related to the various variables I would want to capture from the sample. This is important so as to avoid bias. The selection of persons will be also be based on population demographics which will include age, race as well as gender.

The sample size I will select will be determined by the population size which stands at 4085 as well as study’s purpose which is the determination of a satisfaction survey of employee pay. I plan to use a sample size which is more or the same as that of a study carried previously which is in one way or the other similar to the study I want to conduct now. I will however carry out a detailed review of the various procedures utilized in such a study so as to avoid repeating errors committed in the sample size determination of the previous study.

**References**

Fuller, W.A. (2009). Sampling Statistics. John Wiley and Sons

Levin, J. & Alan, J. (2000). Elementary statistics in social research. Allyn and Bacon