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10.1. In a t
tes
t
for a
single s
ample, the
sample’s
mean
is c
ompared t
o
the
population
.
10.2. When we us
e a paire
d-samples
t test
to
co
m
pare
the pretest
an
d posttest scores
for a group of
45 people, the degrees of freedom (df)
are _____
.
10.3. If we c
onduct a t test for independent
samples, and n1 =
32 and n2 =
35,
the degrees of freedom (df) are _____.
10.4. A researcher
wants
to study t
he e
ffe
ct of college education on people’s earning by comparing the annual salaries of a randomly-select
ed
g
roup
of 100 college graduates to the annual salaries of 100 randomly-selected group of people w
hose
highest leve
l o
f education is high schoo
l. To
compare t
he mean annual salaries of the
two groups
, the r
es
ea
rcher should use a t test for ______
.
10.5. A training coordinator wants to determ
ine the
effectiveness of a pro
gram
that makes extensive
use of educational technology when training new
employees
. She compares the
scores of her new e
mployees who
completed the training on a nationall
y-normed test to the mean s
core of
all those i
n the country who took the same
test. The a
ppropriate
statistic
al test the training coordinator should use for her analysis
is the t
test for ______.
10.6. As part of the process to develop two parallel forms of a q
uestionnaire, the persons creating the questionnaire
may administer both forms to a
group of students, and then use a t test for ______ samples to compare
the mean scores on the tw
o forms.
Circle the correct
answer:
10.7. A differenc
e of 4 points between two homogeneous groups i
s lik
ely to
be more/less
statistically
s
ignifican
t tha
n the same diffe
rence
(of 4
points) between two heterogeneous groups, when all four g
roups a
re
taking completing the same survey and have
approximately the same number of subjects.
10.8. A difference of 3 points on a 100-item test taken by two g
roups is likely to be
more/lessstatistically signi
ficant than a difference of 3 points on a 30-item test taken by the sa
me two
groups.
10.9 When a t test for paired
samples is used to compare the
pretest and the posttest
means, the number of
pretest scores is the same as/different than
the number of post-test scores.
10.10. W
hen we want to compare whet
her females’ scores on the GMAT are
different f
rom males’ scores, we should use a t test for paired samples/independen
t samples.
10.11 In studies where the alternative (
research) hypothesis is directional, the critical
values for a one
tailed test/
two-tailed
test
should be used to determine the level of significance (i
.e., the p
value).
10.12 W
hen the alternative hypothesis is: HA: u1=u2
, the critical va
lues for
one tailed test/two-tailed test should be used to determine the level of statist
ical s
ignificance.
10.13. In a study conducted to compare the test scores of experimental and control g
roups, a 50-item test is administered to both groups at the end of t
he study.
The m
e
an of the ex
perimental group on the test is 1 point higher than the mean of
the control group. The researchers
conduct a t test for independent samples to c
ompare the two means. The obtained t value is 1.89, and the p-value is
.05. C
an we conclude that the experimental treatment was clearly effective because t
he t v
alue is s
tatistically significant? Ex
plain.
10.14. Identify each of the following as a null hypothesis, a directional hypothesis, or a non-directional hypothesis.
a. mean 1does not equal mean 2 is a ______ hypothesis
b. mean 1 does equal mean 2 is a __________hypothesis
c. mean 1 is greater than mean 2 is a ________hypotheses
d. mean 1 minus mean 2 equals zero is a _______hypothesis
10.15. A company psychologist wants to compare the scores of a group of 35
employees on two different IQ tests: one is a group IQ test and one is an individually-administered IQ test. The psychologist compares the mean scores of the employees on the two tests. Which t test should the psychologist use to determine whether there is
a significant difference between the two sets of IQ
scores? Explain.
10.16. The CEO
of ABC Company wishes to determine whether there are differences between union members and manage
rs in their attitude tow
ard
the company. The CEO asks 30 randomly selected union members and 28 managers to complete a 40-item questionnaire designed to measure attitudes towa
rd the company. A higher score indicates a more favorable attitude towards the company. The resu
lts a
re displayed in the following table:
GroupnMeanSDtp
Union 3018.309.85
- 1.92.03
Managers2823.079.07
a. Which t test should the CEO use to compare the responses of the union members and the managers? Explain.
b. What are the degrees of freedom?
c. What are the conclusions of the CEO based on the results in the table? Explain.
10.17. Based on the results of the study described in the previous question, the CEO and the HR manager decide to implement several programs to get the union more actively involved in making decisions at ABC. After implementing the programs for a year, the CEO asks the same group of union members (n=3
0) to about the
ir attitudes towards the company again, using the same questionnaire as the one used the year before. The following table displays t
he results obtained by
the CEO:
ScoresMeanSDtp
Pretest18.309.85
- 7.13.0001
Posttest22.101.26
10.18. A plant manager randomly divides her employees into two groups. One group (
Group A) i
ncludes 32 employees and the second one (Group B) includes 30 e
mployees. A
fter dividing the employees, the manager wants to confirm that t
he two groups are indeed similar in performance. He hypothesizes that there is no statistically significant difference between the two groups. To c
ompare the two groups, the plant manager use ratings given by the employees’ front-li
ne supervisors at the end of the previous y
ear. The rating scale ranges fr
om 5 (excellent employee) to 1 (on the brink of termination). Using these ratings, the manager conducts a t test to determine whether the
two groups are similar. The results are as follows:
|
Group |
Mean |
SD |
|
32 |
3.66 |
1.31 |
|
2.008 |
||
|
30 |
3.00 |
1.26 |
|
t crit(.05,df)=2.0; |
t crit(.02,df)=2.390; |
t crit(.01,df)=2.660 |
- a.Which t test was used and why?
- b.What were the degrees of freedom?
- c.What are the manager’s conclusions? Explain.
10.19. Joe, a new manager suspects that the 23 new em
ployees assig
ned to h
is d
epartment have lower levels of social skills than the new employees hired into
the all the other departments in the rest of the company. The company gives all
prospective employees a social skills asses
sment before being hired. The mean score obtained by Joe’s new employees is 635.13 and the mean score of
all 678
new employees recently hired by the company on the same soc
ial skills as
sessment is 430 (fl=430). A t test is used to compare the social skills assessment scores of Joe’s new employees to all the new employees in the c
ompany. The results of the t test are:
Mean score= 635.13SD= 71.53t value= 3.75 p=.0001
d.
Which t test is used and why?
What are the degrees of freedom (df)?
What are Joe’s conclusions? Explain
11.1. While a t test is used to compare two means, the one-way ANOVA can be used to simultaneously
compare ____ groups.
11.2. An ANOV A is considered to be an extension of the t test for independent samples because both investigate differences between ______.
11.3. By conducting a one-way ANOVA test to compare multiple (more than 2) group means simultaneously instead of conducting a series of t tests to compare these means, the potential level of ____ is reduced.
11.4. In order to apply the ANOV A test, the data should be measured on a(n)
_____ or ______scale .
•
11.5. The one-way ANOV A is used when there is/are ____independent variable(s).
11.6. With 3 groups, the null hypothesis (Ho) in ANOVA is: __________.
11.7. The total (or grand) mean in ANOV A can be thought of as the mean of ____.
11.8. The SSw (within-groups sum of squares) and the SSg (between-groups
sum of squares) are equal to thesum of squares.
11.9. To find the MSg, we divide the SSg by _________.
11.10. To compute the F ratio, we divide the ______ mean square by the
_________
mean square.
11.11. Factorial ANOVA is commonly used when there are at least ______ independent variables.
Circle the correct answer:
11.12. The following is an example of a(n) null/alternative
hypothesis in ANOVA:
Mean one does not equal mean 2 and/or mean one does not equal mean 2 and/or mean 2 does not equal mean 3
11.13. Post hoc comparisons should be conducted in cases where the F ratio
is/is not
statistically significant.
11.14. The F ratio is likely to be statistically significant wh
en the differences between
the group means are small/large.
.
11.15. The F ratio is more likely to be statistically significant when it is used to
analyze scores from groups that are homogenous/heterogeneous
in regard to the characteristic or behavior being measured.
11.16. An ANOVA procedure is used to analyze data from a study comparing scores of three
groups. Following are the obtained mean squares and the appropriate critical values for the F ratio at p=.05 and p=.01
Fcrit(.05,2,20) = 3.49 and Fcrit(.O1,2,20) = 5.85
Compute the obtained F ratio.
Determine whether the results are statistically significant.
Report your conclusions.
11.17. Three different age groups of consumers (ages 18-25, 26-35, 36-45) in two
different regions of the country (Midwest, South) were surveyed about their likelihood of buying a new product. Following are the means and standard deviation
s obtained by the three ag
e groups in each of the two regions:
|
Means |
Standard Deviations |
|||||||
|
Ages |
||||||||
|
Region |
18-25 |
26-35 |
36-45 |
|||||
|
Midwest |
50.2 |
5 |
2.8 |
53.3 |
2.5 |
3.1 |
2.7 |
|
|
South |
41.0 |
48.5 |
55.9 |
3.2 |
Two separate
one-way ANOVA procedures are conducted to tes
t whether the differences between the three means of the three age groups in each of the two regions are statistically significant. Estimate which F ratio would be larger: The
one resulting from
analyzing the survey re
sults obtained from the three age groups in the Midwest or the one from analyzing the survey results obtained by the three age groups in the South explain your answer.
11.18. Three statistics classes at
University A
took the same test as did 3 other
statistics classes at Coll
ege B
. Following are the means and standard deviations of the 3 classes in each of the two schools:
|
SCHOOL |
Stats |
|||||
|
Class I |
Class 2 |
Class 3 |
||||
|
71.4 |
78.8 |
90.2 |
4.3 |
4.8 |
||
|
College B |
72.1 |
78.6 |
8 |
9.3 |
6.6 |
8.7 |
Two separate one-way ANOVA procedures are used to test whether the differences between the means in
each of the two schools are statistically significant. Estimate which F ratio would be larger: the one resulting from analyzing the test scores obtained by the three groups at University A or the one
resulting from analyzing the test scores of the three groups at College B. Explain your answer.
11.19. Each of the two figures below (Figure A and Figure B) depicts a set of 3
distributions. Two separate one-way AN OVA analyses are performed to test whether there are statistically significant differences between the three means in each set and two F ratios are computed. Estimate which of the two F ratios is
likely to be higher and explain your answer.
11.20. In a study comparing means of 4 groups, the F ratio was significant at the p<.05 level. The 4 means are Mean 1=13.12; Mean 2=9.31; Mean 3=13.65; and Mean 4=11.34. Tukey’s post hoc comparison is used to test which means statistically differ from each other. The obtained HSD value at the p=.05 level is 3.74. Which means are statistically significantly different from each other? Explain.
11.21. A pilot-test marketing research study comparing two new models of widgets was conducted in two companies (Company A and Company B). In each of the two companies, one manufacturing plant used one new widget and the other plant used the other new widget. At the end of the year, the employees using the new widgets in their jobs completed a questionnaire assessing their satisfaction with the widgets. Following is a table listing the mean scores of the two plants questionnaire scores for each of the two companies (those that used new widget 1 and those that used new widget 2). Study the data in the table. (Note: Do not attempt to compute the F ratios or the exact level of significance in order to answer the questions below.)
|
Means of |
||
|
Company |
Employees Using |
|
|
Widget 1 |
Widget 2 |
|
|
Company A |
55 |
53 |
|
Company B |
50 |
48 |
- a.Are there differences in questionnaire scores as a result of the using the two widgets? Explain.
- b.Are there differences in questionnaire scores between the two companies?
Explain.
