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.

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Research Question: Does a person's level of education (high school, bachelor's degree, or master's degree) have an impact on their annual income?

Explanation: This question is appropriate for an independent samples t-test because it compares the means of two independent groups (levels of education) and determines if there is a significant difference in their annual incomes.

Variables in this study:

1. Independent Variable: Level of education
- Attributes: Categorical and discrete (high school, bachelor's degree, or master's degree)

2. Dependent Variable: Annual income
- Attributes: Continuous and quantitative (measured in dollars)

The variables fit the qualifications for an independent samples t-test because the independent variable is categorical, and the dependent variable is continuous. The test compares the means of two independent groups (levels of education) to determine if there is a significant difference in the dependent variable (annual income).

Statistical notation and hypotheses:

- Null Hypothesis (H0): There is no significant difference in the annual income based on the level of education.
- Alternative Hypothesis (H1): There is a significant difference in the annual income based on the level of education.

Types of errors that could occur:

1. Type I Error: Rejecting the null hypothesis when it is true, i.e., concluding there is a significant difference in annual income based on education levels when there is none.
2. Type II Error: Failing to reject the null hypothesis when it is false, i.e., concluding there is no significant difference in annual income based on education levels when there is actually a difference.

In order to complete this discussion assignment, you need to follow these steps:

1. Identify an appropriate research question: Start by selecting a research question that was created in Week 1 or choose a new question if none from Week 1 are suitable. Make sure the research question can be answered using a z-test, t-test, or Chi-Square test.

2. Describe why the question is appropriate for the selected statistical test: Once you have chosen a research question, explain why the selected statistical test (z-test, t-test, or Chi-Square test) is appropriate to answer it. Consider the nature of the variables and the assumptions of each test.

3. Identify the variables in the study and their attributes: Identify the variables involved in the research question and describe their attributes. Determine if each variable is discrete or continuous, quantitative or categorical, and the scale of measurement (nominal, ordinal, interval, or ratio). Additionally, determine whether each variable is independent or dependent.

4. Check if the variables fit the qualifications for the selected statistical test: Verify if the variables meet the requirements for the selected statistical test. For example, a z-test typically requires a normally distributed continuous variable, t-tests can be used for continuous variables, and Chi-Square tests are used for categorical variables.

5. List the statistical notation and hypotheses: Write down the statistical notation for the null and alternative hypotheses. The null hypothesis (H0) represents no effect or no difference, while the alternative hypothesis (Ha) states the presence of an effect or difference.

6. Describe the types of errors: Finally, discuss the types of errors that could occur based on the selected statistical test. For example, a Type I error occurs when the null hypothesis is rejected incorrectly, and a Type II error occurs when the null hypothesis is incorrectly accepted.

By completing each step, you should be able to provide all the required information for your initial posting in this discussion assignment.