Prompt: Some people believe that female brains should have different volume from males. Given the data, your job is to perform the appropriate statistical test or procedure and help them decide.

Question: I am having a hard time understanding the correct test to perform to give me the P-Value. Would the correct test be Regression, One-Sided T-Test, or Two-Sided? And in the future how would I know which of these test will give me the proper P-Value?

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√n

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability.

Hope this helps.

To determine the appropriate statistical test for this scenario, we need to consider the specific research question and the type of data we have. In this case, you want to compare the brain volumes between females and males, and the data is likely to be continuous (volumes measured in units such as cubic centimeters).

Since we have two independent groups (females and males), each with their own brain volume measurements, the correct test to use would be an independent samples t-test.

Now, let's address the second part of your question about determining whether to use a one-sided or two-sided test.

If you have a specific directional hypothesis (e.g., you expect female brains to have larger volumes than male brains), you would use a one-sided t-test.

However, if you are simply interested in whether there is any difference between female and male brain volumes, without a specific directional hypothesis, you would use a two-sided t-test. The two-sided test will determine if there is a statistically significant difference in either direction.

To determine which test (one-sided or two-sided) will give you the proper p-value, you need to think about your research question and your specific expectations or hypotheses. If you have a clear expectation about the direction of the difference, then you would choose the corresponding one-sided test. If you are simply interested in whether there is any difference, regardless of the direction, then you would choose the two-sided test.

It's important to note that the choice between one-sided and two-sided tests should be based on sound theoretical reasoning and not done arbitrarily. Understanding the research question and the specific expectations or hypotheses will guide you in making the appropriate choice. Additionally, consulting with a statistics expert or referring to statistical textbooks or resources can be helpful in making this decision.