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Business Analytics. STOP! READ ALL OF THE SYLLABUS MATERIAL ABOUT THE MANAGERIAL REPORTS. Your report must meet all the requirements and format for a Case Problem as described in the syllabus.
The following report is due at the beginning of Exam TWO on Monday, September 24. It must be
handed in as a printed report. Late or emailed hand-ins will receive a grade of zero (no exceptions!). This
is the case even if you completed the report but forgot to print it or bring it to class. Be certain you
staple together all pages of the entire report. You must use the SPSS/MINITAB software where indicated (not
Excel). NOTE: You must do your own work. No collaboration with other students is allowed. You must
not copy, paraphrase, or in any way use someone else’s work.
Managerial Case Problem: “Automobile Assembly Plant” (Worth 20 points total)
Automobile assembly plants have become increasingly automated over the past 25 years. The
management of one United States automobile company recently learned that their competitors are
planning another round of investments in “next generation” robotic automation. They are concerned
that their company’s assembly plant workforce may be inadequately trained and educated to perform
satisfactorily in an ever more technologically advanced factory environment.
As a preliminary assessment of the workforce, the owners have randomly selected a sample of 81
employees. Each person was given a test in basic quantitative skills and the score recorded (under the
variable named “Test Scores”). Also recorded was her/his educational level in number of years of
advanced education completed after high school, using these categories: 0, 1, 2, 3, or 4 (where the
category “4” is understood to mean “4 or more years”; these results are under the variable named
“Years of advanced education”). All sample data are posted on Blackboard as a Minitab worksheet file
named “Test Scores Minitab Data”.
You are to analyze these data by answering the following questions. Number your responses to match
the numbers shown below.
1. How do you describe the distribution of test score data? Do the following:
a. Create a histogram of the test score data using Minitab’s default settings. Describe what you see.
b. Generate for the test scores the values of the median, mean, and standard deviation.
Are the values for the mean and the median close?
c. Generate the Probability Plot. Do the results plot close to a straight line? Is the
p-value > 0.05?
d. What do you conclude about the distribution of test score data?
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2. How do you describe the “Years of advanced education” data? Create either a bar chart or a pie
chart (your choice). Use the “Years of advanced education” as the “Categorical variables” (you
will thus have five categories, namely, the numbers 0 through 4). If you chose a bar chart, then
display the Y axis as “percent”. If you chose a pie chart, then show the slice labels as “percent”.
Describe what you see.
3. What is the 95% two-tailed confidence interval for the population mean test score? Determine
the confidence interval both by manual calculation and by using Minitab/spss.
4. Do you reject or not reject that the population mean test score is equal to 55? Fully explain using
the confidence interval you obtained for question 3.
5. What is the 95% two-tailed confidence interval for the population proportion of people who have
zero years of advanced education? Determine the confidence interval both by manual
calculation and by using Minitab. (Note: You must first obtain the raw counts for persons with
zero years advanced education and with 1 or more years combined. One easy way to do so is to
obtain a Pie chart that has frequency as the slice labels. Use these counts to create a frequency
table in the worksheet. Then follow the instructions that are attached to this case.)
6. Do you reject or not reject that the population proportion of workers with zero years of advance
education is equal to 50%? Fully explain using the confidence interval you obtained for
question 5.
7. Management has learned that the population mean score on this test for the competitors’
workers is 55. The goal of management is that the population mean test score for their plant
workers be greater than 55. You are asked to analyze this issue by answering this question: “Is
there sufficient evidence to reject that the population mean test score for this plant’s workforce
is less than or equal to 55 points?” Answer this by doing the following:
a. Manually conduct a full test of hypothesis at a 5% significance level using the critical
value approach. Use and number all six steps as given in the attachment to this exercise
(also see your text).
b. Next modify steps 4 through 6 to show the p-value approach as given in the attachment
to this exercise (also see your text).
c. Generate the Minitab results for this test of hypothesis and explain how the Minitab
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results compare with your manual calculations and conclusion.
8. Generate the Minitab results for a proportion test of hypothesis using as the alternative
hypothesis that the population proportion of workers with zero years of advanced education is
greater than 50%. Use α = 0.05 and fully explain the Minitab results and what you conclude from
them.
Minitab comments:
NOTE: Before generating the two-tailed t or z confidence intervals, be certain that the alternative
hypothesis is set to “ ≠ “. Do this by clicking Options and then selecting the “ ≠ “ alternative hypothesis.
Be sure the “Perform hypothesis test” box is not checked.
Generate the t two-tailed confidence interval for the population mean as follows:
Go to Stat > Basic Statistics > 1-Sample t …
Click in the variable (the relevant column of data)
Click the Options button. Enter the desired confidence level (entered in percent notation,
e.g., 95). The default is 95%.
Click OK. The Confidence Interval appears in the session window along with other supporting
information.
Generate the two-tailed z confidence interval for the population proportion as follows:
Go to Stat > Basic Statistics > 1 Proportion …
From the drop down menu, select either “One or more samples, each in a column” if your data
is all in a single column or else “Summarized data” if you are using a frequency table.
Click in either the column of data or else the frequency table. If you are using a frequency table,
then enter as “Number of Events” the frequency of the variable of interest and enter as
“Number of trials” the sample size.
Click the Options button. Enter the desired confidence level (entered in percent notation,
e.g., 95). The default is 95%.
Click OK. The Confidence Interval appears in the session window along with other supporting
information.
Generate a test of hypothesis for either a population mean or a population proportion by proceeding as
above except check the “Perform hypothesis test” box and then enter the population value you are
testing. Click Options and select the form of alternative hypothesis you wish for the test.
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Hypothesis Testing
The critical value approach to hypothesis testing:
1. State the null hypothesis ( H0 ) and the alternative hypothesis ( H1 ). Use correct
symbols.
2. Choose the level of significance ( α ) and the sample size ( n ).
3. Determine the appropriate test statistic and sampling distribution.
4. Determine the critical value(s) that divide the rejection and non-rejection regions.
5. Collect the sample data, organize the results, and compute the value of the test statistic.
6. Make the statistical decision and give the technical justification: Either “Reject the H0
because …” (give the test statistic and its value and show using the critical statistic(s)
that the test value is in the rejection region) or else “Do not reject the H0
because …”(give the test statistic and its value and show using the critical statistic(s)
that the test value is in the non-rejection region). Also, state the business or managerial
conclusion in terms of the factual context of the problem.
Modifications to the hypothesis testing steps for the p-value approach:
Steps 1 through 3 are the same. Then …
4. Collect the sample data, organize the results, compute the value of the test statistic, and
then compute its p-value.
5. Make the statistical decision and give the technical justification: Either “Reject the H0
because …” (give the p-value of the test statistic and show that this is less than the value
of α) or else “Do not reject H0 because …” (give the p-value of the test statistic and show
that this is greater than or equal to the value of α). Also, state the business or
managerial conclusion in terms of the factual context of the problem
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