### Confidence Intervals

###### Hypothesis Tests
December 18, 2017
###### Normal Distribution
December 18, 2017

Competency
Given a real-life application, develop a confidence interval for a population parameter and its interpretation.
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 \$40,000 to \$120,000 per year. As a Business Analyst, your boss asks you to research and analyze the salary distributions. You are given a Deliverable3_Spreadsheet.xlsx that contains the following information:
• A listing of the jobs by title
• The salary (in dollars) for each job
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 job titles with yearly salaries ranging from approximately \$40,000 to \$120,000 for the state of Minnesota.
What to Submit
Your boss wants you to submit the spreadsheet with the completed calculations. Your research and analysis should be present within the answers provided on the Deliverable_03_Questions_ma.docx.

Deliverable 03Worksheet
1. Discuss the importance of constructing confidence intervals for the population mean by answering these questions.
o What are confidence intervals?
o What is a point estimate?
o What is the best point estimate for the population mean? Explain.
o Why do we need confidence intervals?
Answer and Explanation:

2. Using the data from the Excel 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.
Answer and Explanation:

3. Using the data from the Excel 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.
Answer and Explanation:

4. Compare your answers for (2) and (3). You notice that the 99% confidence interval is wider. What is the advantage of using a wider confidence interval? Why would you not always use the 99% confidence interval? Explain with an example.
Answer and Explanation:

5. We want to estimate the mean salary in Minnesota. How many jobs must be randomly selected for their respective mean salaries if we want 95% confidence that the sample mean is within \$126 of the population mean and σ = \$1150.
Is the current sample size of the data set in our excel document of 364 large enough? Explain.
Answer and Explanation:

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