whenever a two-tailed test is being conducted, the the rule of thumb requires which signs?
When conducting a two-tailed test, the rule of thumb requires using both positive and negative signs.
Here's how you can understand it step by step:
Step 1: Define the Null and Alternative Hypotheses
- Start by clearly defining the null hypothesis (H₀) and the alternative hypothesis (H₁).
- The null hypothesis represents the claim that you want to test, assuming there is no significant difference or relationship.
- The alternative hypothesis represents the claim that you suspect might be true, suggesting a significant difference or relationship.
Step 2: Set the Level of Significance (α)
- The level of significance, usually denoted as α, determines the critical regions for both tails of the distribution. The common values for α are 0.05 or 0.01.
- For a two-tailed test, you divide α by 2, meaning you split the critical regions between both tails.
Step 3: Determine the Critical Values and Rejection Regions
- Based on the level of significance, look up the critical values from the corresponding distribution table. For example, if you're working with a t-distribution, you need critical t-values.
- Note that critical values are positive when looking in one tail and can be both positive and negative when looking in two tails.
- In a two-tailed test, the critical values are symmetric, meaning they have equal absolute values but opposite signs.
Step 4: Collect Sample Data and Calculate the Test Statistic
- Gather the sample data and calculate the test statistic depending on the type of test being conducted (e.g., t-test, z-test, etc.)
Step 5: Compare the Test Statistic with the Critical Values
- Use the calculated test statistic to compare it with the critical values obtained in Step 3.
- If the test statistic falls outside of the critical values, you reject the null hypothesis in favor of the alternative hypothesis.
- If the test statistic falls within the critical values, you fail to reject the null hypothesis.
In summary, when conducting a two-tailed test, the rule of thumb requires considering both positive and negative signs because you are examining the possibility of a significant difference or relationship in both directions from the null hypothesis.