Correct Answer: C. (a), (c), (b), (d), (e)
Solution:The process of hypothesis testing involves a systematic series of steps to determine whether to reject a null hypothesis (HOH_0HO) based on sample data. The correct sequence, as per the instructions, is outlined below in detail:
(a) Setting the null and alternative hypothesis: This is the foundational step where the researcher specifies the null hypothesis (HOH_OH0), which typically states that there is no effect or no difference between groups or conditions. Alongside, the alternative hypothesis (H1H_1H1) is set, which states that there is an effect, a difference, or a relationship. These hypotheses frame the scope and direction of the statistical analysis.
(c) Determining the appropriate statistical test: Once the hypotheses are defined, the next step involves selecting the correct statistical test that aligns with the data type, distribution, and the hypothesis itself. This choice is crucial as it impacts the analysis' validity. Possible tests include t-tests, chi-square tests, ANOVA, regression analysis, among others, depending on the data's nature and the hypothesis specifics.
(b) Setting the level of significance: After choosing the test, the level of significance (a) is decided. This value defines the threshold for rejecting the null hypothesis. Common levels are 0.05, 0.01, or 0.10, translating into a 5%, 1%, or 10% risk of wrongly rejecting the null hypothesis, respectively. This step sets the critical values for the subsequent statistical test.
(d) Setting the decision rule: Based on the selected level of significance and the chosen statistical test, the decision rule is established. This rule outlines the conditions under which the null hypothesis will be rejected or not rejected, incorporating the test statistic's critical values derived from the statistical test's distribution.
(e) Analyzing the collected data: Finally, with the decision rule in place, the actual data collected through research is analyzed. This analysis involves calculating the test statistic from the data and applying the decision rule. Based on whether the test statistic falls within the critical region, the null hypothesis is either rejected or not rejected, concluding the hypothesis testing process.
Thus, the sequence (C): (a), (c), (b), (d), (e) provides a logical and systematic approach to hypothesis testing, ensuring that the test is properly aligned with the research questions, correctly executed, and that conclusions are based on predetermined criteria, reducing the risk of error in hypothesis testing.