The t Test for Related Samples The t Test for Related  Samples Program Transcript MATT JONES: As  its  name implies, the independent samples  t-­test has  the assumption of the independence of observations. But that's not always  the case. Sometimes  we take multiple observations  of the same unit of analysis, such as  a person, over  time. In this  case, we'll use a paired sample t-­test, sometimes   referred to as  the dependent sample t-­test. Let's go to SPSS  to see how we do this. To perform  the paired sample t-­test in SPSS, we once again go to Analyze, Compare Means, and down to the Paired Sample T-­test. SPSS  doesn't require much information here;; only  the pair  of variables  of which we would like to test. We have a simulated data set here for  statistical anxiety  of students. Students   were provided with an instrument that measures  their  anxiety  around statistical topics  on a number  of different constructs-­-­ teachers, interpretation, asking for   help, worth, and self-­conceptualization. They  were given the test at the beginning of the class  and at the conclusion of a class. Hence, why  in the value labels  we see pre-­test and post-­test. As  a teacher, I might have some interest in determining whether  students  felt more comfortable with me or  had lowering anxiety  over  time. This  is  perfect for  a paired sample t-­ test. To perform  this  paired sample t-­test, we'll go to Analyze, Compare Means, the Paired Sample T-­test. SPSS doesn't ask  for  much information;; only  the pair  of variables  of which I would like to test. In this  case, teacher  pre-­test and teacher  post-­test. So this  is  a classic  before and after. The first piece of output I obtain from  the paired sample t-­test are some descriptive statistics, specifically  around the pairwise comparison I'm looking at, which is  the teacher  subscale pre-­test and post-­test. I see that there is  mean on the pre-­test of 17.32 and on the post-­test, an 18.44. So it appears, at least from  a descriptive sense, that there is  a higher  mean on the post-­test than the pre-­test. On the instrument, higher  scores  on an item  or  the subscale indicate higher  levels  of anxiety  for  that specific  attitude. Except for  this   specific  subscale, fear  of statistics  teachers, where higher  scores  actually   indicate lower  levels  of anxiety. So if post scores  are higher  than pre scores, that means  on average, students   feel lower  levels  of anxiety  and more positive attitude about their  statistics   teacher. I can see here, at least from  a descriptive sense, that that appears  to be the case. But from  the sample, I am  performing a test of statistical significance. Next to the mean, I'm provided with the sample size 25-­-­ 25 observations  pre-­test and 25 observations  post-­test, all the same person-­-­ the standard deviation for   the pre-­test and the post-­test, and the standard error  of the mean. ...

1. The t Test for Related Samples
The t Test for Related Samples
Program Transcript
MATT JONES: As its name implies, the independent samples
t--test has the
assumption of the independence of observations. But that's not
always the case.
Sometimes we take multiple observations of the same unit of
analysis, such as a
person, over time. In this case, we'll use a paired sample t-

2. -test, sometimes
referred to as the dependent sample t--test. Let's go to SPSS to
see how we do
this.
To perform the paired sample t--test in SPSS, we once again go
to Analyze,
Compare Means, and down to the Paired Sample T--test. SPSS
doesn't require
much information here;; only the pair of variables of which
we would like to test.
We have a simulated data set here for statistical anxiety of
students. Students
were provided with an instrument that measures their anxiety
around statistical
topics on a number of different constructs---- teachers,
interpretation, asking for
help, worth, and self--conceptualization.
They were given the test at the beginning of the class and at
the conclusion of a
class. Hence, why in the value labels we see pre--test and post-
-test. As a teacher,
I might have some interest in determining whether students
felt more comfortable
with me or had lowering anxiety over time. This is perfect
for a paired sample t--
test. To perform this paired sample t--test, we'll go to Analyze,
Compare Means,
the Paired Sample T--test.
SPSS doesn't ask for much information;; only the pair of
variables of which I
would like to test. In this case, teacher pre--test and teacher
post--test. So this is a
classic before and after. The first piece of output I obtain from

3. the paired sample
t--test are some descriptive statistics, specifically around the
pairwise comparison
I'm looking at, which is the teacher subscale pre--test and
post--test.
I see that there is mean on the pre--test of 17.32 and on the
post--test, an 18.44.
So it appears, at least from a descriptive sense, that there is a
higher mean on
the post--test than the pre--test. On the instrument, higher
scores on an item or the
subscale indicate higher levels of anxiety for that specific
attitude. Except for this
specific subscale, fear of statistics teachers, where higher
scores actually
indicate lower levels of anxiety.
So if post scores are higher than pre scores, that means on
average, students
feel lower levels of anxiety and more positive attitude about
their statistics
teacher. I can see here, at least from a descriptive sense, that
that appears to be
the case. But from the sample, I am performing a test of
statistical significance.
Next to the mean, I'm provided with the sample size 25---- 25
observations pre--test
and 25 observations post--test, all the same person---- the
standard deviation for
the pre--test and the post--test, and the standard error of the
mean.
©2016 Laureate Education, Inc. 1

4. The t Test for Related Samples
Next, let's go down and interpret the paired sample test itself.
We can see that on
average, there was a difference of 1.12 units on the scale with
a standard
deviation of 2.50. From the 95% confidence interval, we see
that the true
difference is somewhere between 2.15 and 0.085. We have a t-
-statistic of 2.235
and an associated p--value of 0.035.
At the 0.05 level, the results are statistically significant and
we can say that there
is a significant difference between pre--test scores and post-
-test scores.
Therefore, we can reject the null hypothesis that there is no
difference. On
average, it appears on the post--test, students had lower levels
of anxiety about
their statistics teacher.
This last example illustrated that students felt more
comfortable with statistics as

5. time progressed and specifically felt less anxious about their
statistics instructor. I
certainly hope this example rings true for you, and that you
feel comfortable or at
least don't self--identify as being anxious about statistics at
the conclusion of this
course. I encourage you to review your textbook, review the
videos, ask your
instructor for help, and also research the resources here
available at Walden
University to help you succeed.
©2016 Laureate Education, Inc. 2
Question #1 (10 points) Southern Hospital Supplies, a company
that makes hospital gowns, is considering capacity expansion.
The new facility would produce a new type of gown, and
currently the potential or marketability for this product is
unknown. If a large plant is built and a favorable market exists,
a profit of $100,000 could be realized. An unfavorable market
would yield a $90,000 loss. However, a medium plant would
earn a $60,000 profit with a favorable market. A $10,000 loss
would result from an unfavorable market. A small plant, on the
other hand, would return $40,000 with favorable market
conditions and lose only $5,000 in an unfavorable market. Of
course, there is always the option of doing nothing. Recent
market research indicates that there is a .4 probability of a
favorable market, which means that there is also a .6 probability
of an unfavorable market.
With this information, please use the decision tree technique to
select the alternative that will result in the highest expected
monetary value.

6. Question #2 (10 points) Management wants to design an
assembly line that will turn out 800 videotapes per day. There
will be eight working hours in each day. The industrial
engineering staff has assembled the information below:
Task
Time (min.)
Immediate Follower
a
.2
b
b
.2
f
c
.4
e
d
.1
e
e
.3
f
f
.2
h
g
.1
h
h
.2
i
i
.6

7. none
A) Determine the optimum cycle time (i.e., actual operating
time/desired output).
B) What is the minimum number of stations needed?
C) Assign tasks to work stations.
D) What is the efficiency of this assembly line?
Question #3 (10 points) Four samples of three observations each
have been taken, with actual measurements (in centimeters)
shown below. Construct x bar and R charts, and determine if the
production process is under control.
Samples
1
2
3
4
12.3
11.9
12.0
12.1
12.2
12.2
12.2
11.8
12.1
12.2
11.8
11.8

8. Question #4 (10 points) John has been asked to determine
whether the $22.50 cost of tickets for the community dinner
theater will allow the group to achieve break-even and whether
the 175 seating capacity is adequate. The cost for each
performance of a 10-performance run is $2,500. The facility
rental cost for the entire 10 performances is $10,000. Drinks
and parking are extra charges and have their own price and
variable costs, as shown below:
1
2
3
4
5
6
7
8
9
Selling Price (P)
Variable Cost (V)
Percent Variable Cost (V/P)
Contribution 1-(V/P)
Estimated Quantity of Sales Units
Dollar (Sales Sales*P)
Percent of Sales
Contribution Weighted by Percent Sales (col.5*col.8)
Tickets with Dinner
$22.50
$10.50

9. 175
Drinks
$5.00
$1.75
175
Parking
$5.00
$2.00
100
Will the theatre break even?

10. Question #5 (10 points) Attendance at Los Angeles’s newest
Disneylike attraction, Vacation World, has been as follows:
Quarter
Guests (in thousands)
Quarter
Guests (in thousands)
Winter ‘11
73
Summer ‘12
124
Spring ‘11
104
Fall ‘12
52
Summer ‘11
168
Winter ‘13
89
Fall ‘11
74
Spring ‘13
146
Winter ‘12
65
Summer ‘13
205
Spring ‘12
82
Fall ‘13
98
Compute seasonal indices using all of the data.
Question #6 (10 points) Consider the following transportation
decision-making information:

11. Plant
Capacity
Store
Demand
A
400
X
200
B
500
Y
250
C
100
Z
300
Total
1000
Total
750
Cost to ship from plant to store (per unit of demand)
Plant
Store
X
Y
Z
A
$2
$2
$3.5
B
$4
$5
$4.5

12. C
$3
$3
$3
a) Develop the following shipping assignment table that uses
the Solver function to find the optimal shipping patterns
between the plants and the stores.
Plant
Store
X
Y
Z
A
B
C
b) What is the minimal shipping cost?
Question #7 (10 points) The annual demand for an item is
10,000 units. The cost to process an order is $75 and the annual
inventory holding cost is 20% of item cost. What is the optimal
order quantity, given the following price breaks for purchasing
the item? What price should the firm pay per unit? What is the

13. total annual cost at the optimal behavior?
Quantity
Price
1 – 9
$2.95 per unit
10 – 999
$2.50 per unit
1,000 – 4,999
$2.30 per unit
5,000 or more
$1.85 per unit
Question #8 (10 points) The MGT 504 course introduces you to
basic Operations Management concepts and their
implementations. I cannot hope to detail each concept. My goal
here is to make you aware of as many concepts as possible in
order to prepare you for many varied career pursuits, so you
may have a moment of clarity in your daily work, “Oh yes, we
touched on that in Operations Management” and with that you
have a stepping stone to exploring the concept in depth.
Could you find any potential applications of OM concepts or
skills to your daily work or personal life? Please give me some
details.

14. The t Test for Related Samples
The t Test for Related Samples
Program Transcript
MATT JONES: As its name implies, the independent samples
t--test has the
assumption of the independence of observations. But that's not
always the case.
Sometimes we take multiple observations of the same unit of
analysis, such as a
person, over time. In this case, we'll use a paired sample t-
-test, sometimes
referred to as the dependent sample t--test. Let's go to SPSS to
see how we do
this.
To perform the paired sample t--test in SPSS, we once again go
to Analyze,
Compare Means, and down to the Paired Sample T--test. SPSS
doesn't require
much information here;; only the pair of variables of which

15. we would like to test.
We have a simulated data set here for statistical anxiety of
students. Students
were provided with an instrument that measures their anxiety
around statistical
topics on a number of different constructs---- teachers,
interpretation, asking for
help, worth, and self--conceptualization.
They were given the test at the beginning of the class and at
the conclusion of a
class. Hence, why in the value labels we see pre--test and post-
-test. As a teacher,
I might have some interest in determining whether students
felt more comfortable
with me or had lowering anxiety over time. This is perfect
for a paired sample t--
test. To perform this paired sample t--test, we'll go to Analyze,
Compare Means,
the Paired Sample T--test.
SPSS doesn't ask for much information;; only the pair of
variables of which I
would like to test. In this case, teacher pre--test and teacher
post--test. So this is a
classic before and after. The first piece of output I obtain from
the paired sample
t--test are some descriptive statistics, specifically around the
pairwise comparison
I'm looking at, which is the teacher subscale pre--test and
post--test.
I see that there is mean on the pre--test of 17.32 and on the
post--test, an 18.44.
So it appears, at least from a descriptive sense, that there is a
higher mean on

16. the post--test than the pre--test. On the instrument, higher
scores on an item or the
subscale indicate higher levels of anxiety for that specific
attitude. Except for this
specific subscale, fear of statistics teachers, where higher
scores actually
indicate lower levels of anxiety.
So if post scores are higher than pre scores, that means on
average, students
feel lower levels of anxiety and more positive attitude about
their statistics
teacher. I can see here, at least from a descriptive sense, that
that appears to be
the case. But from the sample, I am performing a test of
statistical significance.
Next to the mean, I'm provided with the sample size 25---- 25
observations pre--test
and 25 observations post--test, all the same person---- the
standard deviation for
the pre--test and the post--test, and the standard error of the
mean.
©2016 Laureate Education, Inc. 1

17. The t Test for Related Samples
Next, let's go down and interpret the paired sample test itself.
We can see that on
average, there was a difference of 1.12 units on the scale with
a standard
deviation of 2.50. From the 95% confidence interval, we see
that the true
difference is somewhere between 2.15 and 0.085. We have a t-
-statistic of 2.235
and an associated p--value of 0.035.
At the 0.05 level, the results are statistically significant and
we can say that there
is a significant difference between pre--test scores and post-
-test scores.
Therefore, we can reject the null hypothesis that there is no
difference. On
average, it appears on the post--test, students had lower levels
of anxiety about
their statistics teacher.
This last example illustrated that students felt more
comfortable with statistics as
time progressed and specifically felt less anxious about their
statistics instructor. I
certainly hope this example rings true for you, and that you
feel comfortable or at
least don't self--identify as being anxious about statistics at
the conclusion of this
course. I encourage you to review your textbook, review the
videos, ask your
instructor for help, and also research the resources here
available at Walden

18. University to help you succeed.
©2016 Laureate Education, Inc. 2