What are the steps espoused by Applied Statistics in Business and Economics for formal hypothesis testing? Explain why the sequence is important. What might happen if the hypothesis test is performed before the researcher has decided on the significance level?

Twenty students randomly assigned to an experimental group receive an

instructional program; 30 in a control group do not. After 6 months, both groups
are tested on their knowledge. The experimental group has a mean of 38 on the
test (with an estimated population standard deviation of 3); the control group
has a mean of 35 (with an estimated population standard deviation of 5). U

The steps espoused by Applied Statistics in Business and Economics for formal hypothesis testing generally follow the following sequence:

1. State the Hypotheses:
- The first step is to clearly state the null hypothesis (H0) and alternative hypothesis (Ha) based on the research question. The null hypothesis represents the status quo or no effect, while the alternative hypothesis suggests a specific effect or relationship.

2. Formulate an Analysis Plan:
- In this step, the researcher decides on the appropriate statistical test to use, identifies the necessary sample size, and determines the significance level (α), also known as the Type I error rate. The significance level represents the maximum probability of rejecting the null hypothesis when it is true.

3. Collect and Analyze the Data:
- Data that is relevant to the research question is collected, often using a controlled experiment or random sampling. The collected data is then analyzed using the chosen statistical test.

4. Interpret the Results:
- Based on the analysis, the researcher interprets the results and determines whether to reject the null hypothesis or fail to reject it. This decision is made by comparing the calculated test statistic to the critical value(s) obtained from probability tables or using statistical software.

5. Make a Decision:
- Finally, a decision is made regarding the research question based on the interpretation of the results. If the null hypothesis is rejected, there is evidence to support the alternative hypothesis. If the null hypothesis is not rejected, there is insufficient evidence to support the alternative hypothesis.

The sequence of these steps is important because it provides a structured and systematic approach to conducting hypothesis tests. It ensures that the researcher follows a logical and coherent process, minimizing errors and enhancing the credibility of the findings. Each step builds upon the previous ones, allowing for a clear progression from problem formulation to decision-making.

If a hypothesis test is performed before the researcher decides on the significance level, it can lead to potential issues. The significance level dictates the probability of rejecting a true null hypothesis, and it's an important consideration in hypothesis testing. If the significance level is not predetermined, the researcher might be inclined to choose a level that gives a favorable result for their hypothesis, leading to potential bias or manipulation of the findings. Having a predetermined level, established before analyzing the data, adds objectivity and ensures a fair assessment of the evidence.