Testing Hypotheses
The process of conducting a hypothesis test is structured into important phases. They are, in order, formulating null (H0) and alternative (Ha) hypotheses, selecting a significance level (α), choosing an appropriate statistical test, collecting data, and computing the test statistic (Anderson et al., 2018). After that, one can compare it to a critical value or calculate the p-value to distinguish statistical significance. Based on the importance of Type I and Type II errors, experimenters specify a significance level (α), with 0.05 or 0.01 being common values (Anderson et al., 2018). This decision balances the risk of incorrectly rejecting the null hypothesis with the risk of failing to reject it when it is false.
Hypothesis tests can be calculated with statistical software such as R, Python, SAS, SPSS, and Stata. The statistical tables that correspond to the selected significance level and test contain the critical test values (Cleff, 2020). These values are used to determine whether the scrutinized test statistic falls within the critical region for rejection (Cleff, 2020). The null hypothesis is rejected if the computed test statistic is inside the rejection zone or if the p-value is less than the significance threshold.
Application to Business Settings
For example, a business can evaluate the impact of a new marketing agenda on earnings. The decision to enforce the campaign would follow the rejection of the null hypothesis (Illowsky & Dean, 2022). It would indicate that the program does not affect sales if the hypothesis test shows a significant increase in sales relative to the control group.
In a different situation, a business might look into whether customer satisfaction levels differ between two product iterations. If the hypothesis test did not show a statistically significant difference in satisfaction levels, the null hypothesis, which claims that there is no difference, would not be rejected (Illowsky & Dean, 2022). This would suggest that the customer satisfaction levels of the two versions are comparable.
For a third example, a business also wants to determine whether a new manufacturing process affects the average weight of its product. In this case, a two-tailed test is appropriate because the alternative hypothesis predicts a shift in either direction (Illowsky & Dean, 2022). In a two-tailed test, the rejection region includes extreme values in both tails of the distribution, allowing the detection of any meaningful departure from the null hypothesis.
References
Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2018). Modern business statistics (6th ed). Cengage Learning.
Cleff, T. (2020). Applied statistics and multivariate data analysis for business and economics: A Modern Approach Using SPSS, Stata, and Excel. Springer.
Illowsky, B., & Dean, S. (2022). Introductory statistics. Openstax.