Research Question and Hypotheses
- Research question: Is the mean monthly salary of male CEOs in the United States higher than that of females?
- Ho (null hypothesis): The average monthly salary earned by male CEOs in the U.S. is statistically no more than the average monthly salary earned by their female counterparts.
- Ha (alternative or research hypothesis): The mean monthly wages of male CEOs in the U.S. are higher than those of female CEOs.
The Role of the Equality Sign in the Null Hypothesis
The equal sign of the null hypothesis (Ho) conveys the presumption that there is no observable difference between the two groups being compared. It is predicated on the hypothesis that any observed differences are due to sampling error rather than real population differences (Bennett, Briggs, and Trioa, 2003). To ascertain if the alternative hypothesis is supported by the data, statistical analysis and hypothesis testing often begin with the null hypothesis. The null hypothesis could be rejected if the findings indicate that the alternative hypothesis is more likely to be true (Tendeiro & Kiers, 2019).
Interpreting Results When the p-Value Exceeds the Alpha Level
The null hypothesis, which states that the mean monthly income of male CEOs in the United States is equal to or less than the mean monthly salary of female CEOs, is not rejected because the p-value is not smaller than the alpha value of.05 (Bennett, Briggs, and Trioa, 2003). Hence, there is no adequate data to conclude that the mean monthly salaries of American male and female CEOs differ statistically significantly. To thoroughly investigate this problem, another study with a larger sample size or a different approach may be required.
Consequences of Incorrectly Rejecting the Null Hypothesis
Importantly, it would be a Type I error to incorrectly reject the null hypothesis (Bennett, Briggs, and Trioa, 2003). In this case, the null hypothesis would be disregarded even if it were true. Thus, the incorrect conclusion that there is a substantial disparity in CEO pay between men and women could be made. When the alpha level is set too high, this type of error, often called a false positive, increases the likelihood that the null hypothesis will be rejected even if it is true (Tendeiro & Kiers, 2019).
References
Bennett, J. O., Briggs, W. L., & Triola, M. F. (2003). Statistical reasoning for everyday life. Boston, MA: Addison-Wesley.
Tendeiro, J. N., & Kiers, H. A. (2019). A review of issues about null hypothesis Bayesian testing. Psychological methods, 24(6), 774.