# Deliverable 3 – Confidence Intervals Assignment Content Competency Develop a confidence interval for a population parameter. Instructions Scenario (in

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## Assignment Content

1. Competency
Develop a confidence interval for a population parameter.

Instructions
Scenario (information repeated for deliverable 01, 03, and 04)
A major client of your company is interested in the salary distributions of jobs in the state of Minnesota that range from \$30,000 to \$200,000 per year. As a Business Analyst, your boss asks you to research and analyze the salary distributions. You are given a spreadsheet that contains the following information:

• A listing of the jobs by title
• The salary (in dollars) for each job
• Deliverable 3 – Confidence Intervals.xlsx

You have previously explained some of the basic statistics to your client already, and he really liked your work. Now he wants you to analyze the confidence intervals.

Background information on the Data
The data set in the spreadsheet consists of 364 records that you will be analyzing from the Bureau of Labor Statistics. The data set contains a listing of several jobs titles with yearly salaries ranging from approximately \$30,000 to \$200,000 for the state of Minnesota.

What to Submit

## Question 1

1. Discuss the importance of constructing confidence intervals for the population mean by answering these questions.

a. What are confidence intervals?

b. What is a point estimate?

c. What is the best point estimate for the population mean? Explain.

d. Why do we need confidence intervals?

## Question 2

 Calculations/Values Formulas/Answers Mean Standard Deviation n Critical Value Margin of Error Lower Limit Upper Limit

2. Using the data from the ‘Data’ tab in this workbook, construct a 95% confidence interval for the population mean. Assume that your data is normally distributed and σ is unknown. Include a statement that correctly interprets the confidence interval in context of the scenario.
Hint: Use the sample mean and sample standard deviation from Deliverable 1. Do NOT copy and paste the values. Instead, use cell referencing to use the unrounded values.

Calculate all of the values needed to create this confidence interval to the right.

Below, include a breakdown of the steps, include formulas, and correctly interpret the solution in context of the scenario with the correct units.

## Question 3

 Calculations/Values Formulas/Answers Mean Standard Deviation n Critical Value Margin of Error Lower Limit Upper Limit

3. Using the data from the ‘Data’ tab in this workbook, construct a 99% confidence interval for the population mean. Assume that your data is normally distributed and σ is unknown. Include a statement that correctly interprets the confidence interval in context of the scenario.
Hint: Use the sample mean and sample standard deviation from Deliverable 1. Do NOT copy and paste the values. Instead, use cell referencing to use the unrounded values.

Calculate all of the values needed to create this confidence interval to the right.

Below, include a breakdown of the steps, include formulas, and correctly interpret the solution in context of the scenario with the correct units.

## Question 4

4. Compare your answers for Question 2 and 3. Notice that the 99% confidence interval is wider.

a. What is the advantage of using a wider confidence interval?

b. Why would you not always use the 99% confidence interval? Explain with an example.

## Question 5

CV (z)
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