This document provides a review and preparation guide for the GM 533 Final Exam. It summarizes the topics covered in each week of the course, including descriptive statistics, probability, confidence intervals, hypothesis testing, simple and multiple regression. It provides sample questions and worked examples for key concepts like the binomial distribution, hypothesis testing, and confidence intervals. Students are directed to use Excel templates to solve problems involving the normal distribution.

1. Preparing for the
GM 533 Final Exam
Professor Brent Heard

2. GM 533 Final Exam Prep
• Summary of topics covered
– Week 1 - Descriptive Statistics: includes central tendency, dispersion, and the
shape of the distribution, in numbers, pictures, and tables.
– Week 2 – Probability: includes 3 major problem types, and their most
important variations: contingency tables, expected value, and the binomial
distribution.
– Week 3 – Probability continued: includes the normal distribution, its
application to sampling distributions, and its most important variations.
– Week 4 – Confidence intervals and sample size determinations, and their most
important variations.
– Week 5 – Hypothesis testing: includes the 5-step hypothesis testing
procedure, applied to means and proportions, and its most important
variations.
– Week 6 – Simple linear regression: includes interpreting Minitab output for
point estimates, hypothesis tests, and confidence intervals.
– Week 7 – Multiple regression: includes the same elements as simple
regression, but also includes the application to multiple independent
variables.
• Examples and topic areas follow

3. GM 533 Final Exam Prep
• Sample Question on Binomial Distribution
– Assume that a study was done finding that 70 percent of males in Georgia are
football fans. If a researcher asks 8 Georgia Males if they are fans, the
following binomial distribution would be applicable. What is the probability
that at least 5 will be football fans?
n p
8 0.7
x P( x) Cumulative
0 0.0001 0.0001
1 0.0012 0.0013
2 0.0100 0.0113
3 0.0467 0.0580
4 0.1361 0.1941
5 0.2541 0.4482
6 0.2965 0.7447
7 0.1977 0.9424
8 0.0576 1.0000

4. GM 533 Final Exam Prep
• Sample Question on Binomial Distribution
– Assume that a study was done finding that 70 percent of males in Georgia are
football fans. If a researcher asks 8 Georgia Males if they are fans, the
following binomial distribution would be applicable. What is the probability
that at least 5 will be football fans?
n p
8 0.7
“At least 5” is the probability that 5, 6, 7
or 8 will be fans. Simply add those
x P( x) Cumulative probabilities.
0 0.0001 0.0001
1 0.0012 0.0013
2 0.0100 0.0113 0.2541
3 0.0467 0.0580 0.2965
4 0.1361 0.1941 0.1977
My total is 0.8059
5 0.2541 0.4482 0.0576 or about 81% which
6 0.2965 0.7447 is the probability of
7 0.1977 0.9424 SUM 0.8059
at least 5 being
8 0.0576 1.0000
football fans.

5. GM 533 Final Exam Prep
• Analysis Example
– 9 members of the local college baseball team had the following number for
extra base hits for the year. Using the Minitab output given, determine:
A. Mean
B. Standard Deviation
C. Range
D. Median
E. The range of the data that would contain 68% of the results.
Data
7
9
4
24
15
17
15
6
29
– Minitab Follows

6. GM 533 Final Exam Prep
Descriptive Statistics: Extra Base Hits
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
Extra Base Hits 9 0 14.00 2.82 8.47 4.00 6.50 15.00 20.50
Variable Maximum
Extra Base Hits 29.00
This is technically NOT
Stem-and-Leaf Display: Extra Base Hits the correct Median.
Stem-and-leaf of Extra Base Hits N = 9 A. Mean
Leaf Unit = 1.0 B. Standard Deviation
C. Range (Max – Min = 29 – 4 = 25)
D. Median (I would enter data into Excel to
4 0 4679
find the Median is 15 or do by ordering
(3) 1 557
2 2 49 data and identifying)
E. The range of the data that would contain
68% of the results. (Mean – Std Dev,
Mean + Std Dev) which is (14 – 8.47, 14 +
8.47) or (5.53,22.47)

7. GM 533 Final Exam Prep
Here I used
=MEDIAN(A1:A9)
It returned the median of 15.

8. GM 533 Final Exam Prep
• Sample Question on Hypothesis Testing
– Pepito’s Pizza Works is putting pizzas out by delivery as fast as they
can. Pepito’s claims they can deliver pizzas within their delivery area in
less than 29 minutes. You are given the following data from a sample.
Sample size: 120 Deliveries
Population standard deviation: 1.4
Sample mean: 28.3
Formulate a hypothesis test to evaluate the claim.

9. GM 533 Final Exam Prep
• Sample Question on Hypothesis Testing
– Pepito’s Pizza Work is putting pizzas out by delivery as fast as they can.
Pepito’s claims they can deliver pizzas within their delivery area in less
than 29 minutes. You are given the following data from a sample.
Sample size: 120 Deliveries
Population standard deviation: 1.4
Sample mean: 28.3
Formulate a hypothesis test to evaluate the claim.
– Answer: Ho: µ ≥ 29, Ha : µ < 29
– (In this case, the claim was Ha)
– Remember Ho always contains equality (It will either be =, ≤ or ≥)
– Ha will be either ≠, < or >

10. GM 533 Final Exam Prep
• Confidence interval Example
– Acme computers needs to find a new vendor for
their hard drives. They are considering using
Howie’s Hard Drives as a vendor. Acme’s
requirement is that 95% of the hard drives last
24000 hours ± 2000 hours. The following data is
from an independent source who evaluated
Howie’s. Should Acme buy from Howie’s? Explain
your answer. (Follows on next page)

11. GM 533 Final Exam Prep
• Mean = 24500
• Sample Standard Deviation 2250
• Min 21402
• Max 29463
• Margin of Error 4500
• Answer Follows

12. GM 533 Final Exam Prep
• No, Acme shouldn’t buy from Howie’s looking
at their requirements (24000 – 2000, 24000 +
2000) which is (22000, 26,000). Based on the
results given, Howie’s would yield a tolerance
of (24500 – 2*2250, 24500+2*2250) which is
(20000, 29000). This does not meet Acme’s
requirement. You could also see this by
looking at the margin of error.

13. GM 533 Final Exam Prep
• Example on Pivot/Contingency Tables
• The table below gives the number of cars of
various colors and the state tag on the car for
a parking lot in a mall close to DC.
VA MD DC Other State Total
Blue 4 8 9 3 24
Black 9 7 11 8 35
White 12 14 21 15 62
Other 37 10 29 35 111
Total 62 39 70 61 232

14. GM 533 Final Exam Prep
• Based on the table, find the probability that a
car is from VA or MD.
• Based on the table, given that a car is from
DC, find the probability it is black.

15. GM 533 Final Exam Prep
VA MD DC Other State Total Find the probability that a car is
Blue 4 8 9 3 24 from VA or MD. Add 62 + 39 to get
Black 9 7 11 8 35 So the answer would be 91/232 or it’s
White 12 14 21 15 62 decimal form.
Other 37 10 29 35 111
Total 62 39 70 61 232
62 + 39 = 91

16. GM 533 Final Exam Prep
VA MD DC Other State Total
Given that a car is from DC, find
Blue 4 8 9 3 24
the probability it is black.
Black 9 7 11 8 35
Given that it is from DC means we are only
White 12 14 21 15 62 dealing with the 70 cars from DC.
Other 37 10 29 35 111 There are 11 of those that are black, so the
Total 62 39 70 61 232 probability is 11/70

17. GM 533 Final Exam Prep
• Normal Distribution Example
– The number of students who use the dining hall at
an urban college on a given day is normally
distributed with a mean of 1578 students and a
standard deviation of 274 students.

18. GM 533 Final Exam Prep
• I’m suggesting Excel to work these types of
problems even if you are given partial Minitab
results.
• Go to
http://highered.mcgraw-
hill.com/sites/0070620164/student_view0/exc
el_templates.html
And download the template titled Normal
Distribution.

19. GM 533 Final Exam Prep
• It will look something like this when you open
it

20. GM 533 Final Exam Prep
• Before doing anything else, click the “Review” tab
at the top of Excel (Between Data and View), then
click “Unprotect Sheet”.
After clicking
“Unprotect
Sheet” it will say
“Protect Sheet.”
Leave it that way
and save to your
computer. You
now have a cool
Normal
Distribution
Calculator.

21. GM 533 Final Exam Prep
• Back to our problem….
• Questions
• What is the probability that less than 1400
students will use the dining hall?
• What is the probability that more than 1700 will
use the dining hall?
• What is the probability that between 1400 and
1600 students will use the dining hall?
• Get that Normal Distribution Excel Calculator
ready and be amazed!

22. GM 533 Final Exam Prep

23. GM 533 Final Exam Prep

24. GM 533 Final Exam Prep
This gives
This gives you area to
you area to the right
the left based on
based on your mean
your mean and
and standard
standard deviation.
deviation.
This gives
you area
between
two values
based on
your mean
and
standard
deviation.

25. GM 533 Final Exam Prep
I entered
I entered 1700 in the
1400 in the green cell
green cell which gives
which gives me the
me the probability
probability of more
of less than than 1700
1400 students
students using the
using the dining hall.
dining hall. The answer
The answer is 0.3281
is 0.2580 I entered 1400 in the left cell and
1600 in the right green cell which
gives me the probability of between
1400 and 1600 students using the
dining hall. The answer is 0.2740

26. GM 533 Final Exam Prep
• Another Confidence Interval Example
– I randomly sampled 18 engineers where I work and asked
them how many projects they have worked on in the last
five years. The sample mean was 21, with a standard
deviation of 5. What is the mean number of projects of all
engineers at my research center? Why? What is the 95%
confidence interval for the population mean? You are
given the information below from Minitab.
One-Sample T
N Mean StDev SE Mean 95% CI
18 21.00 5.00 1.18 (18.51, 23.49)

27. GM 533 Final Exam Prep
• Another Confidence Interval Example
– I randomly sampled 18 engineers where I work and asked them
how many projects they have worked on in the last five years.
The sample mean was 21, with a standard deviation of 5. What
is the mean number of projects of all engineers at my research
center? Why? What is the 95% confidence interval for the
population mean? You are given the information below from
Minitab.
Answer:
21 projects would be the best estimate for the mean. I
would expect 95% of the population mean to fall between
18.51 and 23.49 projects. The t is used because of the
sample size.

28. GM 533 Final Exam Prep
• Regression Example
– I did an analysis to determine if the number of
hours studied for a final exam related to the Final
Exam grade for students. On the sheets that
follow you will see what my Minitab results were.

29. General Regression Analysis: Final Grade versus Hours of Analysis of Variance
Study
Source DF Seq SS Adj SS Adj MS F P
Regression Equation Regression 1 8090.71 8090.71 8090.71 171.274
0.000000
Final Grade = 34.2845 + 1.45508 Hours of Study Hours of Study 1 8090.71 8090.71 8090.71 171.274
0.000000
Error 22 1039.25 1039.25 47.24
Coefficients Lack-of-Fit 18 936.58 936.58 52.03 2.027 0.259215
Pure Error 4 102.67 102.67 25.67
Term Coef SE Coef T P Total 23 9129.96
Constant 34.2845 3.38091 10.1406 0.000
Hours of Study 1.4551 0.11118 13.0872 0.000
Fits and Diagnostics for Unusual Observations
Summary of Model Final
Obs Grade Fit SE Fit Residual St Resid
S = 6.87303 R-Sq = 88.62% R-Sq(adj) = 88.10% 24 19 37.1947 3.17993 -18.1947 -2.98609 R
PRESS = 1426.21 R-Sq(pred) = 84.38%
R denotes an observation with a large standardized residual.

30. GM 533 Final Exam Prep
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 48.8353 2.41382 (43.8294, 53.8413) (33.7280, 63.9426)
Values of Predictors for New Observations
Hours
of
New Obs Study
1 10

31. GM 533 Final Exam Prep
I did an analysis to determine if the number of hours studied for a final exam related to the
Final Exam grade for students. On the sheets that follow you will see what my Minitab
results were.
Answer the following questions.
Determine the regression equation.
What conclusions are possible using the meaning of bo (intercept) and b1 (regression coefficient) in this
problem?
What does the coefficient of determination (r-squared) mean?
Calculate the coefficient of correlation and explain what it means.
Does this data provide significant evidence (a=0.05) that the final exam grade is associated with the hours
studied? Find the p-value and interpret.
Determine the predicted grade for someone who spends 10 hours studying for the final exam.
What is the 95% confidence interval for the score for spending 10 hours studying on the test? What conclusion is
possible using this interval?

32. GM 533 Final Exam Prep
I did an analysis to determine if the number of hours studied for a
final exam related to the Final Exam grade for students. On the
sheets that follow you will see what my Minitab results were.
Answer the following questions.
Determine the regression equation. y= 34.2845 + 1.45508x
What conclusions are possible using the meaning of bo (intercept) and b1
(regression coefficient) in this problem? For each hour of study the final grade
is increased by about 1.5 points (1.45508). bo represents the y intercept or
34.2845 in our case. It is the score that a student could expect to get without
studying.
What does the coefficient of determination (r-squared) mean? The .886 means
that 88.6 percent of the variability of the final grade can be explained by the
number of study hours. The other 11.4% would be due to something else or
be unexplained.

33. GM 533 Final Exam Prep
Calculate the coefficient of correlation and explain what it means. Square Root of
(0.886) is 0.942 which is r, the correlation coefficient. With a value this close to
one, we could say there is strong positive correlation.
Does this data provide significant evidence (a=0.05) that the final exam grade is
associated with the hours studied? Find the p-value and interpret. Yes, the p value
was 0. If it were above 0.05, I would have said “no.”
Determine the predicted grade for someone who spends 10 hours studying for the
final exam. 48.8353
What is the 95% confidence interval for the score for spending 10 hours studying
on the test? What conclusion is possible using this interval? (43.8294, 53.8413)
We would be 95% confident that if someone studied for 10 hours they would
score on average between those two values.

34. GM 533 Final Exam Prep
• Multiple Regression
– Be able to identify the multiple regression output
from a Minitab analysis
• Equation
• F value
• p value
• Confidence intervals
• (Basically reading from Minitab output)

35. GM 533 Final Exam Prep
• I will post these charts in the “Stat Cave” at
– www.facebook.com/statcave
– Good Luck!