RD – z, t, or Chi-Square Test Study
Background
During this week you will work in your group discussion area to identify a research question created in week 1 that would utilize any of the following: z test, t test for single sample, independent samples t test, repeated measures t test, or Chi-Square test. This discussion will help you work towards your “RD - Week 3 Assignment”. If there are no research questions that fit any of these types of statistical analyses, you will need to decide on a new question before moving forward with the assignment.
Discussion Assignment Requirements
Initial Posting – In your initial posting for this assignment, include the following:
• Identify an appropriate research question that would require the use of a z, t, or Chi-Square test to answer. Pick the question from the list created in week 1 or identify a new question if there are no appropriate ones from week 1.
• Describe why this question is appropriate for the selected statistical test.
• Identify the variables in this study and each of their attributes: discrete or continuous, quantitative or categorical, scale of measurement (nominal, ordinal, interval, or ratio), and independent or dependent.
• Do the variables fit the qualifications for the selected statistical test? Explain.
• List the statistical notation and written explanation for the null and alternative hypotheses.
• Describe the types of errors that could occur.
whaaaaaaat??
To answer this question, you will need to understand the concepts of z-tests, t-tests, and Chi-Square tests.
A z-test is used when you have a sample larger than 30 and can assume that the population standard deviation is known. It is typically used to compare a sample mean to a known population mean.
A t-test is used when you have a small sample size (less than 30) or when the population standard deviation is unknown. It is used to compare two means, either from two independent groups or from a single group measured at two different times.
A Chi-Square test is used to determine if there is a significant association between two categorical variables.
Now, let's address the requirements of the discussion assignment:
1. Identify an appropriate research question: Pick a question from the list created in week 1 or come up with a new question if none of them are appropriate. This research question should require the use of a z-test, t-test, or Chi-Square test to answer.
For example, let's say the research question is: "Is there a significant difference in the mean test scores of students who attended an after-school tutoring program compared to those who did not attend?"
2. Describe why this question is appropriate for the selected statistical test: This question is appropriate for an independent samples t-test because we are comparing two groups (students who attended the tutoring program vs. those who did not) to see if there is a significant difference in their mean test scores.
3. Identify the variables and their attributes: In this study, the independent variable is "attendance at the after-school tutoring program" (categorical, nominal), and the dependent variable is "test scores" (continuous, interval or ratio).
4. Do the variables fit the qualifications for the selected statistical test? Yes, the variables fit the qualifications for an independent samples t-test since we have two independent groups and a continuous dependent variable.
5. List the statistical notation and hypotheses:
- Null hypothesis (H0): There is no significant difference in the mean test scores between students who attended the after-school tutoring program and those who did not attend (μ1 = μ2).
- Alternative hypothesis (Ha): There is a significant difference in the mean test scores between students who attended the after-school tutoring program and those who did not attend (μ1 ≠ μ2).
6. Describe the types of errors that could occur: In hypothesis testing, two types of errors can occur:
- Type I error: Rejecting the null hypothesis when it is true (false positive).
- Type II error: Failing to reject the null hypothesis when it is false (false negative).
By addressing these requirements, you can effectively design and analyze a research study using a z-test, t-test, or Chi-Square test to answer your research question.