Question

what is the primary reason for setting a significance level before conducting a hypothesis test?
a. to calculate the mean of the sample data.
b. to choose the appropriate statistical test.
c. to decide the threshold for rejecting the null hypothesis.
d. to determine the sample size needed for the study.

Explanation:

The significance level ($\alpha$) in a hypothesis test is the probability of rejecting the null hypothesis when it is actually true (Type - I error). It sets a threshold. If the p - value (probability of obtaining the test statistic or more extreme results assuming the null hypothesis is true) is less than or equal to $\alpha$, we reject the null hypothesis.

• Option a: The mean of the sample data is calculated using the formula $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, and it has nothing to do with the significance level.
• Option b: The type of data (e.g., categorical vs. numerical), the research design (e.g., independent samples vs. paired samples), and the distribution of the data (e.g., normal distribution) are factors in choosing a statistical test, not the significance level.
• Option c: This is correct. The significance level $\alpha$ is the threshold. For example, if $\alpha = 0.05$, we reject the null hypothesis when $p\leq0.05$.
• Option d: Sample size is determined by factors such as the effect size, the power of the test (related to Type - II error), and the variance of the population (for numerical data), not directly by the significance level.

Answer:

c. To decide the threshold for rejecting the null hypothesis.