This document contains a multiple choice test with 10 questions about statistics concepts such as descriptive statistics, inferential statistics, measures of central tendency, and sampling. It also includes 3 word problems involving statistical calculations and analyses such as computing measures of central tendency and dispersion, hypothesis testing using z-tests and t-tests, ANOVA testing, and regression analysis. The respondent is asked to work through the problems, show calculations, state hypotheses and decisions, and interpret results.

1. Part I Multiple Choice: Answer each of the Following:
1) A public opinion poll that gauges the popularity of the
President of the United States is an example of:
a. descriptive statistics
b. inferential statistics
c. analytical statistics
d. reductionist statistics
2) Inferential statistics are necessary in research because:
a. it may be impossible to find all members of a certain
population
b. social scientists don't usually have the time or money to test
an entire population
c. some of the population might not cooperate
d. samples are sometimes accurate representations of the
population but can't always be used to generalize
3) In a positively skewed distribution the mean is:
a. equal in value to the median
b. greater in value than the median
c. less in value than the median
d. either a or b, depending on the value of the mode
4) The sum of the squared differences between the scores and
the mean is:
a. 0
b. 1
c. a minimum
d. both a and c
5) As a distribution of scores becomes more variable, the value
of the standard deviation
a. decreases

2. b. stays the same
c. increases
d. becomes unpredictable
6) Within a distribution of scores, measures of dispersion
provide an indication of:
a. the number of cases which are unsatisfactory
b. variety
c. the size of the sample
d. the adequacy of the selection criteria for the sample
7) Your score on the test is the same as the third quartile (Q3).
You may conclude that:
a. you scored higher than 75% of the people who took the test
b. the distribution of the scores is skewed
c. your score is "typical" since it is the same value as the
median
d. you scored higher than 25% of the people who took the test
8) A sampling technique that allows you to ensure proportional
representativeness in a sample is:
a. representative sampling
b. stratified sampling
c. systematic sampling
d. simple random sampling
9) When created, categories of nominal level variables should
be:
a. mutually exclusive to avoid ambiguity in classifying cases
b. exhaustive so that every case fits into a category
c. relevant to the research goals
d. all of the above
10) The median of a distribution of scores represents the score
that is:
a. half of the sum of the scores

3. b. the most common score
c. the middle score
d. half of the difference between the highest and the lowest
scores
Part II Problems:
1. The following data are the monthly rental prices for a sample
10 unfurnished studio apartments in the center of Concord, New
Hampshire, and a sample of 10 unfurnished studio apartments in
Charleston, West Virginia:
Concord
$955 $1,000 $985 $980 $940 $975 $965 $999 $1,247 $1,119
Charleston
$750 $775 $725 $705 $694 $725 $690 $745 $575 $800
a. For each set of data, compute the mean, median, mode, range,
interquartile range, standard deviation, and coefficient of
variation.
b. What conclusions can you draw about unfurnished studio
apartments renting in Concord versus Charleston? Compare and
contrast.
2. In a city of 5,000 adults, 2,000 live in private homes while
the remaining live in apartment buildings. Of those living in
private homes, 240 are upper income, 1,200 are middle income
and 560 are lower income. Of those living in apartment
buildings, 900 are upper income, 600 are middle income, and
1,500 are lower income.
a. Set up a cross-classification table for type of dwelling unit
and income status, to find the probability that a person chosen

4. at random:
a. Is middle income
b. Lives in an apartment building
c. Lives in a private home and is upper income
d. Lives in an apartment building or is lower income
e. Is middle income, if it is known that he lives in an apartment
building
f. Is type of dwelling unit statistically independent of income?
3. There are ten teams in a newly reorganized local baseball
league. If league administrators are necessary to run this
summer league:
a. From among individual team leaders, how many ways are
there to select a league principal administrator, an assistant
league administrator and a team coordinator?
b. How many ways are there to select three individual team
leaders to participate in the league’s administrative activities?
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Name:
_________________________________________________
Date: _____________
Instructions:
The following 11questions are the take-home portion of the
Final Exam. You are allowed to use your books, notes,
calculators, MS Excel, Minitab, and/or any other materials on
ECN to answer the questions. As in the business world, you
may collaborate with your classmates (but NOT tutors or

5. outside help) regarding the problems, but you must turn in your
own completed work. Your answers may be submitted either in
written format or electronic (Word or PDF file format).
Possible partial credit may be given if you show your work,
formulas, and/or assumptions. Feel free to add more paper /
space as needed.
IMPORTANT: Your work can be submitted in either hard copy
or electronic format (e.g. email attachment, ECN) in class on
October 9th, 2013, or via electronic format by midnight on
Saturday, October 12th, 2013.
1. The waiting time for patients at a local hospital emergency
department follows a normal distribution with a mean of 55
minutes and a population standard deviation of 15 minutes. The
quality-assurance department found in a sample of 50 patients
that the mean waiting time was 54 minutes. At the 0.025
significance level, decide if the sample data support the claim
that the mean waiting time is less than 55 minutes.
State the null and alternative hypotheses.
State the decision rule.
Based on the sample data, state your decision in terms of the
null hypothesis (reject or not reject). You
may use either method, comparing the test statistic to the
critical value, or the p-value approach.
2. A machine makes ball bearings for use in other industrial
machinery. The mean diameter of a particular type of ball
bearing is 50 millimeters. Based on a new vendor for their raw
materials, the Quality Assurance manager is worried that the
current production runs will be outside of specification. To test
this, 100ball bearings (n = 100) were sampled. The mean of the
sample is 51.2 millimeters and the SAMPLE standard deviation

6. is1.223 millimeters. Decide if the sample data supports the
claim that the mean diameter is 50 millimeters. Use a 0.02
level of significance.
State the null and alternative hypotheses.
State the decision rule.
Based on the sample data, state your decision in terms of the
null hypothesis (reject or not reject). You may use either
method, comparing the test statistic to the critical value, or the
p-value approach.
3. Based on the Nielsen ratings, the local CBS affiliate claims
its 11:00 PM newscast reaches 41% of the viewing audience in
the area. In a survey of 100 viewers, 36% indicated that they
watch the late evening news on this local CBS station. If =
0.01, what is our decision:
State the null and alternative hypotheses.
State the decision rule.
Based on the sample data, state your decision in terms of the
null hypothesis (reject or not reject).
4. A study by a bank compared the average savings of
customers who were depositors for three years or less, with
those who had been depositors for more than three years. The
results of a sample are:
< 3 Years
> 3 Years
Mean Savings Balance
$1,200
$1,250
Population Standard Deviation
$100
$250
Sample Size

7. 100
150
Calculate the test statistic, z.
5. Given the following hypothesis test:
100 soil samples were taken from the bottom of Lake Erie,
where 70 samples (X1) contained high levels of bacteria. 150
soil samples were taken from the bottom of Lake Superior,
where 90 samples (X2) contained high levels of bacteria.
Using a significance level of 0.05, test the hypothesis:
State the decision rule.
What is the pooled proportion?
Compute the test statistic value.
What is the decision regarding the null hypothesis?
6. An investigation of the effectiveness of a training program
to improve customer relationships included a pre-training and
post-training customer survey. Seven customers were randomly
selected and completed both surveys. The results follow:
Customer
Pre-training survey
Post-training survey
A
6
8
B
5
5
C
10
10
D

8. 7
10
E
6
8
F
5
6
G
2
8
What is the value of the test statistic, t?
7. Suppose that an automobile manufacturer designed a
radically new lightweight engine and wants to recommend the
grade of gasoline that will have the best fuel economy. The four
grades are: below regular, regular, premium, and super
premium. The test car made three trial runs on the test track
using each of the four grades, and the miles per gallon were
recorded:
Below Regular
Regular
Premium
Super Premium
36.69
39.31
38.99
40.04
40.00
39.87
40.02
39.89
41.01
39.87

9. 39.99
39.93
a. Create and show a single-factor ANOVA table with a 0.05
b. Given that the null and alternative hypotheses are:
Based on the ANOVA table F statistics, what is the decision
regarding the null hypothesis?
8. The college of business was interested in comparing the
attendance for three different class times for a business
statistics class. The data follow:
a. Create and show a two-factor ANOVA table with a 0.05level
b. What is the critical F statistic for testing the hypothesis of
c. Given that the null and alternative hypotheses are:
Based on the ANOVA table F statistics, what is the decision
regarding the null hypothesis?
9. Two research labs were asked to test the battery life in hours
of 3 different experimental batteries. Each lab performed 3
tests per battery type with the following results.
BatteryType 1

10. BatteryType 2
BatteryType 3
Lab 1
10.50
7.75
8.75
9.50
7.00
8.00
10.75
8.25
9.00
Lab 2
6.75
4.75
6.75
7.75
5.50
5.75
6.50
5.75
6.25
a. Create and show a two-factor with interaction (replication)
There are 3 rows per sample.
b. Based on the ANOVA table for Interaction, is there a
statistically significant interaction between the labs and battery
types (justify using either the F statistics or the p-value
approach).

11. 10. Given the following table:
Current Length of Employment (Years)
Number of Workdays Absent
5
2
6
3
9
3
4
5
2
7
2
7
0
8
a. Develop and state an estimate (predictor) equation for Ŷ
given X. You can calculate the a and b constants using any
method, manual, Excel, Regression analysis, etc.
b. Based on the estimate equation in part a, what is the
estimated number of workdays absent given a worker who has
been employed for 7 years?
c. Determine the correlation coefficient.
d. Perform a t-Test for the significance of the correlation
coefficient for a two-tailed test with 0.05 level of significance
e. Determine the coefficient of determination.
f. Determine the standard error of the estimate.
11. Given the following table:

12. Labor Hours applied
Labor Cost
1000
$50755
945
$40622
850
$46111
1250
$77000
1300
$68190
1590
$75000
1425
$68444
1350
$71235
1650
$90673
1700
$101182
a. Create a scatter plot of the data.
b. Which is the independent variable?
c. Which is the dependent variable?
d. Does the data show a positive or negative correlation between
X and Y?
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