Introduction
All case studies address the following points:
a.
define the problem statement
The problem we are addressing here is whether Riverside differs from California as
a whole in terms of it’s labor data on age and number of weeks employed for all
workers who recently found a job.
b.
define any and all assumptions made to address the case study
I’m not sure what your looking for here. We are assuming that our small sample
represents Riverside as a whole and that the Riverside Labor force is directly
comparable to the CA labor force. We are also making no effort whatsoever to
accommodate the case that Riverside may have a completely different industrial
structure than the rest of CA as a whole. So these numbers may be meaningless.
c.
analyze the data utilizing concepts and knowledge relevant to this course
See results below.
d.
describe the specific recommendations or solution
See results below.
e.
answer the assigned questions of the case.
See results below.
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
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.
Given the descriptive statistics generated below we can see that the mean for
“weeks employed” is slightly higher than that of California in general. The
standard error for this parameter appears to be reasonably small. Our Kurtosis
and Skewness suggest a fairly normal distribution though slightly positively
skewed. Our data for Age is similar though the distribution is slightly more
Kurtotic with a little better skewness.
Age
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Confidence
Level(99.0%)
Weeks Employed
37.75
2.974194569
37.5
25
11.89677828
141.5333333
1.171432688
0.337401965
36
23
59
604
16
8.764137815
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Confidence
Level(99.0%)
18.6875
2.188452174
18.5
21
8.753808695
76.62916667
0.216255336
0.52260057
30
6
36
299
16
6.448769914
b. Develop a 99% confidence interval estimate of the mean age of newly hired
employees.
I think the output on excel is the amount we want to add to our mean to get the
exact range. So that would be 37.75 – 8.76 to 37.75 + 8.76 or
28.99 to 46.51
so this is our 95% confidence interval for Age.
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?
As we can see from our hypothesis test we fail to reject the null so we can’t say
Riverside is any different than California as a whole. I used the formula
t-stat = (mean – null) / Standard Error
or
(18.6875-17)/2.188452174 = .771 which is below any critical value. So we fail to
reject the null that Riverside is different than California at 99% confidence.
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.
Here we get a correlation coefficient of .796 between age and weeks employed so
there appears to be a positive relationship between the variables. This may imply
older workers find work faster.
e.
Cut and paste your results from EXCEL into your paper.
f.
See the EXCEL spreadsheet with the data to get you started