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Business Statistics: Relationship between Confidence Intervals & Hypothesis Testing

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What is the relationship between confidence intervals and hypothesis testing? How are they the same? How are they different?

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What is the relationship between confidence intervals and hypothesis testing? How are they the same? How are they different?

There exists a close relationship between confidence intervals and hypothesis testing. When we construct a 90 % confidence interval to estimate a population parameter, all values in the interval are considered probable values for the parameter being estimated. Values outside the interval are rejected as relatively improbable.

If the value of the parameter specified by the null hypothesis is contained in the confidence interval so constructed ...

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(See attached file for full problem description)

Answer questions in green.

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Answer these questions below (a, b, c, d, & e) about the case study:

All case studies address the following points:
a. define the problem statement
b. define any and all assumptions made to address the case study
c. analyze the data utilizing concepts and knowledge relevant to this course
d. describe the specific recommendations or solution
e. answer the assigned questions of the case.

Answer this question also:
Then, after solving the case study, emphasize how you can use this technique to solve business problems. What business decisions will you be able to make using this type of analysis?

Case Study
ABC Corporation of California publishes a variety of statistics, including the number of individuals who got a new job during the past 12 months and the mean length of time the individuals have been on the job. The Statistical Analysis Department of ABC Corporation reported that the mean length of time of newly employed individuals in California was 17.00 weeks.
A local Chamber of Commerce for the City of Riverside has commissioned a study on the status of employment in the Riverside area. A sample of 16 employed residents of Riverside included data on the age and the number of weeks on a job. A portion of the data collected in October 2001 is shown as follows:

Age Weeks Employed Age Weeks Employed
55 21 25 6
30 18 40 21
23 11 25 13
52 36 25 11
41 19 59 34
25 12 49 27
42 7 33 18
45 25 35 20

Use EXCEL to answer these questions:

In a 700-1,050-word analysis, address the following:
a. Based on the above data, use descriptive statistics to summarize the data. Use EXCEL to generate your statistical results.
b. Develop a 99% confidence interval estimate of the mean age of newly hired employees.
c. Conduct a hypothesis test to individuals and determine whether the mean duration of employment in Riverside is greater than the California mean duration of 17.00 weeks. Use a .01 level of significance. What is your conclusion?
d. Is there a relationship between the age of a newly employed individual and the number of weeks of employment? Explain. For this case analysis, just answer the above questions in your prepared paper.
e. Cut and paste your results from EXCEL into your paper.
f. See the EXCEL spreadsheet with the data to get you started.
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