# Scenario Module #3

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### Question Description

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 \$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

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

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 worksheet.

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Robert__F
School: Cornell University

Deliverable 03 Worksheet
1. Discuss the importance of constructing confidence intervals for the population mean by
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?
Confidence intervals represent the extreme values within which there is a known
probability or confidence of finding the parameter of the population defined by the
confidence interval. For example, a 95% confidence interval for the population mean
implies that there is a 95% probability that the population mean will be within the
minimum and maximum limits established by the confidence interval. Point estimates, on
the other hand, refer to the value of an estimate of the population. In the previous
example, a point estimate would indicate that the population mean has a specific value,
corresponding to the value of such point estimate. In contrast with the confidence
interval, the point estimate does not give an idea of the confidence that such value is truly
the population mean.
The best point estimate for the population mean is generally the average or mean of a
sample of data taken from such population. However, such claim presumes that the
sample of data collected to estimate the population mean is representative from the
population. Taking this into account, we need confidence intervals because they provide

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 Ο 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.

Sample mean:
π₯Μ =

β π₯π
= \$71,879
π

Sample standard deviation:
β(π₯π β π₯Μ )2
π =β
= \$23,367
πβ1
Z statistic corresponding to a 95% confidence level: 1.96
Confidence interval:
π = π₯Μ Β± π§ β

π
βπ

= 71879 Β± 1.96 β

23367
β364

= (\$69,479 β \$74,280)

The calculated result indicates that there is a 95% confidence in that the population mean
will be contained between \$69,479 and \$74,280.

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 Ο 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.

Sample mean:
π₯Μ =

β π₯π
= \$71,879
π

Sample standard deviation:
β(π₯π β π₯Μ )2
π =β
= \$23,367
πβ1
Z statistic corresponding to a 99% confidence level: 2.58
Confidence interval:
π = π₯Μ Β± π§ β

π
βπ

= 71879 Β± 2.58 β

23367
β364

= (\$68,725 β \$75,034)

The calculated result indicates that there is a 99% confidence in that the population mean
will be contained between \$68,725 and \$75,034.

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.
As observed f...

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