The paper "Statistics for Managers" is a wonderful example of an assignment on management. Initially, the business field dealt with only one population mean and a single proportion. However, there are instances when two random populations might be involved; two population means and two population proportions. Thus, this type of inferential statistics has a number of applications in business. For instance, it can be used to study the market share of a single product in two markets, to the difference in the proportion of male and female customers in a given market or comparing the female proportion of customers in two different markets (different geographic locations).
Therefore, this technique is essential in the day to day business operations since it can be used to identify potential markets for businesses. Moreover, it can be used to test the difference in two proportions whenever researchers are interested in finding the comparison of certain characteristics in one population and the same characteristics in a second population. This makes it crucial to business contexts. According to Black (2009), a group of researchers tried to find out whether there was a difference in the perception of CEOs and consumers on business ethics.
He considered the difference in the proportions of the two groups who believed that the fear of losing their jobs or being caught is among the factors influencing ethical business behaviors. From the entire study, 0.57 of the consumers agreed that the fear of losing a job or being caught has a relatively strong influence on ethical behavior whereas 0.50 of the CEOs had the same feeling. Thus, if this data is determined from a sample of seven hundred and fifty-five (755) consumers and six hundred and sixteen (616) CEOs, we can determine if a higher proportion of consumers than that of the CEOs say that fear has a greater effect on ethical behavior. Therefore, using the hypothesis, Ho: P1 – P2 = 0 vs.
H1: P1 – P2 > 0 where p1 represents the proportion of consumers and P2 that of CEOs. From the z tables, the critical value is 1.28. Thus, since the calculated z statistic is larger than the table value, we fail to accept the null hypothesis and conclude that the proportion of consumers is more than that of CEOs. For a study across two populations, I would use a sample of 1000 in each population since large sample size is associated with accuracy in the projection of what the whole population looks like.
For instance, if I perform an interview on 1000 people and only 500 of them agree that fear has an impact on the general ethical behavior; this number might either be 52% or 48%. On the other hand, if the same interview is performed on 100 people and 50 of them agree that fear has an influence on the ethical behavior, this number might either be 57% or 43%.
So, comparing the two sizes, the larger sample size is quite accurate.