Purpose:
The purpose of this assignment is to solve two inferential analysis problems: determine a confidence interval and perform an hypothesis test on the data in the same data set usefd for Assignments #1 & #2. Plan the analysis, do the calculations and write up the findings.
Determination a 1-Sample Confidence Interval is Task 2a and a 2-Sample Hypothesis Test is Task 2b. These are based on the same data set for the previous assignments. There are two main parts:
• Part A: Inferential Statistics Data Plan and Analysis
• Part B: Write up of Results

Deadline:

Part A: Data Plan and Analysis
Determine a 1-sample confidence interval of your own choosing that is of interest for the data chosen and a 2-Sample Hypothesis Test too. Summarize them and the data to be used briefly in a summary paragraph. It will then be straightforward to complete the following tasks.

➢ Task 1: Select Variables. Review the variables you used for assignments #1 and #2. Determine parameters of interest (such as a mean or means or a proportion or proportions). You may want to base your choice on the scenario you used before or decide on whatever else you may be interested to do with the data.
Select either all the data or your qualitative socioeconomic variable as your grouping variable. Keep in mind that a data set of 30 or more is generally considered to be satisfactory for use of the z-distribution even if the population distribution is not normal (via the Central Limit Theorem). If less than 30, the t-distribution is used when the population standard deviation is not known. Select one (or two, if preferred) expenditure variables from the variables in the data.
Fill in Table 1: Variables Selected for Analysis with name, description, and type of variable (i.e., qualitative or quantitative). You may use a format of your own choosing instead as long as you provide the same information.

➢ Task 2a: 1-Sample Confidence Interval. For one expenditure variable, select and run the appropriate method for estimating a parameter based on a statistic from the sample.
Table 2a: Confidence Interval Information and Results: describe your work, noting the following:
• Random variable stated in words
• Confidence interval method, including rationale and assumptions
• Method used for analyzing data (i.e., web applets, Excel, TI calculator, etc.).
• Results obtained
• Interpretation

➢ Task 2b: 2-Sample Hypothesis Test. Using the second expenditure variable (with the socioeconomic variable as the grouping variable), select and run the appropriate method for making decisions about two parameters relative to observed statistics (i.e., two sample
hypothesis test method).

Table 2b: 2-Sample Hypothesis Test Analysis, describe your work noting the following:

• Hypotheses (null and alternative).
• Two sample hypothesis testing method, including rationale and assumptions
• Method used for analyzing data (i.e., web applets, Excel, TI calculator, etc.).
• Results obtained.
• Interpretation (i.e., Reject the null hypothesis or Fail to reject null hypothesis)

Step 2: Write Up Results

Suggested (but not required) Format: Part B of the Assignment #3 Template
You may use a format of your own choosing instead as long as you provide the same information.

Address the following area:
➢ Introduction. Based on the scenario you submitted for the second assignment, provide a brief description of scenario, including the variables that were used in this analysis. Include a completed “Table 1: Variables Selected for Analysis to show the variables you selected for analysis.
➢ Data Set Description and Method Used for Analysis. Briefly describe the data set, using information provided with data set and write up in Assignment #2. Also describe what method(s) (i.e., free web applets, Excel, TI Calculator) you used to analyze the data.

➢ Results. In this section, you will briefly report the results of your inferential statistics data analysis.

For the Confidence Interval Analysis, write one paragraph that includes:
• Statistical method used, including rationale and whether assumptions were met.
• Statistical Interpretation. The statistical interpretation is that the confidence interval has a probability (1−α, where α is the complement of the confidence level) of containing the population parameter.
• Real World Interpretation. Explain the results in everyday language as in the homework problems.
For the Two Sample Hypothesis Test Analysis, write one paragraph that includes:
• Hypotheses that were assessed.

• Statistical method used, including rationale and whether assumptions were met.
• Conclusion from the Results. This is where you state whether to reject Ho or fail to reject Ho including the p-value that was obtained. The rule is: if the p-value < α, then reject Ho. If the p-value ≥α, then fail to reject Ho.
• Real World Interpretation. Explain, in everyday language, the results. If any of the assumptions were not met, describe how it might affect conclusions. Address issues of Type I and/or Type II Error, where appropriate.

Discussion– Write one brief paragraph that summarizes the results of your findings and how they may be helpful to the person described in the scenario.
Assignment Submission: Name the file that contains your completed Assignment #3 Inferential Statistics Analysis: “Assignment 3 – Student Last Name”. Submit it in the /Assignments/ Tab in the “Assignment #3” folder.

General Grading Rubric Guidelines

Part A: Prepare Data Plan, Analyze Data, and Complete Part A of the Template
Selection of variables and completion of table 10%
Selection and Calculation of Confidence Interval Analysis:
• Selection of Appropriate Test and Rationale
• Assumptions
• Method Used and Calculation
• Conclusion
• Statistical Interpretation 20%
Selection and Calculation of Two Sample Hypothesis Test:
• Research Question and Hypotheses
• Selection of Appropriate Test and Rationale
• Assumptions
• Method Used and Calculation
• Conclusion, including p-value
• Statistical Interpretation 20%
Part B: Write Up of Results
Introduction and Description of Data Set 5%

Confidence Interval. Summarized:
• Statistical method used, including rationale and whether assumptions were met
• Statistical Interpretation
• Real World Interpretation. 15%
Two Sample Hypothesis Test. Summarized:
• Hypotheses
• Statistical method used, including rationale and whether assumptions were met.
• Conclusion from the Results.
• Real World Interpretation. 15%
Discussion 5%
Wrote clearly, concisely, and with few errors. Easy to understand. 10%

Sample Solution