USA: +1(669)289-8683 
Sign in
This hmwk must be delivered in SPSS format.
Assignment 3
CORRELATION
Fill in the blanks:
8.1.
The magnitude of the correlation is indicated by the correlation _____ which can range from -1.00 to +1.00.
8.2. The most common and efficient way to present the correlations of several variables with each other is by using a(n) ______ table.
8.3. The correlation between two variables can be shown graphically by a ________.
8.4. The null hypothesis predicts that the correlation coefficient is equal to _______.
8.5. The Spearman rank order correlation is used when the variables to be correlated are measured on a(n) ______ scale.
Circle the correct answer:
8.6. The hypothesis that states that r0 is an example of a(n)
alternative/null
hypothesis.
8.7. When an increase in one variable is associated with a decrease in the other variable, the correlation between these two variables is
positive/negative
.
8.8. In order to use the Pearson product-moment correlation, the variables to be correlated should be measured on an
ordinal/interval
scale.
8.9. When the points on a scattergram go from the bottom left to the top right they represent a
positive/negative
correlation.
8.10. The true correlation between two variables may be underestimated when the variance of one of the variables is
very high/very low
.
8.11. When the null hypothesis is rejected at p<.001, it means that the chance that r=0 is very small/very high .
8.12. The null hypothesis is rejected when the obtained correlation coefficient is higher/lower than the critical value.
Answer/compute the following questions:
8.13 Which correlation coefficient (a or b) shows a stronger relationship between the two variables being correlated?
a. X1&Y1: r = .85
b. X2&Y2: r = -.94
8.14. Following are two scattergrams (in Figure A and in Figure B). Four different correlation coefficients are listed under each scattergram. Choose the coefficient that best matches each scattergram.
Y
Y
X X
Figure A Figure B
A1. r= .50 B1. r= -.57
A2. r= .78 B2. r= .92
A3. r= -.10 B3. r= .38
A4. r= -.89 B4. r= -.91
8.15 Following is a scattergram showing the scores of 8 statistics students on two tests, X and Y. Each of the first 7 students is represented by a dot and their scores are listed in the table that follows. Use the scattergram to find the scores of student #8 on test X and test Y. The location of this student on the scattergram is represented by a large dot (•) next to number 8.
Y
1
4
4
5 2
3
6 8
2
7 3
1
X
1 2 3 4 5
Student #
X
Y
1 2 4
2 3 3
3 2 1
4 5 4
5 2 3
6 2 2
7 1 1
8 ? ?
8.16 What do these two scattergrams have in common?
Y Y
8.17 Estimate (
do not calculate!
) the correlation between the advertising spending and sales that were obtained over a 5 year span. Indicate whether the correlation is positive or negative, and whether it is high or low. Explain your answer.
Year Ad Spending Sales
1 $21,000 $83
2 15,000 70
3 17,000 68
4 25,000 90
5 19,000 74
8.18 Estimate (
do not calculate!
) which of the two sets of consumer research studies (A&B or X&Y) has a higher correlation. Explain your answer.
Set 1 Set 2
Study #
A B Study # X Y
1 41 50 1 66 47
2 41 47 2 53 36
3 38 43 3 50 45
4 30 39 4 48 38
5 28 37 5 45 39
8.19 Match the correlation coefficient and the diagram illustrating this correlation.
a. r = .91
b. r = .28
c. r = .15
8.20. Study the following intercorrelation table. Two surveys measure consumer attitudes and two surveys measure marketers’ promotional spending. Knowing that Test 1 measures consumer attitudes, speculate which is the other consumer attitudes survey (2, 3, or 4) and which two surveys measure marketers’ promotional spending. (
A hint: the two consumer attitudes surveys should correlate higher with each other than with the two marketers’ promotional spending surveys, and the two marketers’ promotional spending surveys should correlate higher with each other than with the two consumer attitudes surveys.)
2
3
4
1
.35
.89
.23
2
.39
.92
3
.34
8.21. Following are results from a study correlating gross domestic product (GDP) and the Consumer Price Index (CPI) from a group of 16 Asian countries, a group of 15 European countries, and the two groups combined.
Group
Correlation (r)/
Group Size (n)/
Significance (p value)
Asia
r =.59
n = 16
p =.02
Europe
r =.52
n = 15
p =.05
Combined
r =.53
n = 31
p =.01
a. Which correlation coefficient is the highest?
b. Which correlation coefficient has the highest statistical significance?
c. How can a correlation of r=.53 (from the combined group) be more statistically significant (better p value) than a correlation of r=.59 (from the Asian countries)?
Chapter 9
PREDICTION AND REGRESSION
Fill in the blanks:
9.1. In simple regression, there is/are _____ predictor(s).
9.2. The regression line is also called a line __________.
9.3. The slope of the regression line is represented by the letter ___.
9.4. When the regression equation is used to draw a line, the point where that line intersects the vertical line (the Y-axis) is represented by the letter ___ which indicates the intercept.
9.5. When the correlation between two variables is perfect and positive, and we use one of these variables to predict the other one, the standard error of estimate (SE) is _____.
9.6. The difference between an actual Y score and its corresponding predicted Y score (Y’) is called the _____ score.
9.7. In multiple regression with two predictors, there is/are _____ intercept(s), represented in the equation by the letter a.
Circle the correct answer:
9.8. In regression, the predictor is called the
independent/dependent
variable, and the predicted variable (or the criterion variable) is called the
independent/dependent
.
9.9. The predicted variable is represented by the letter
X/Y
and the predictor is represented by the letter
X/Y
.
9.10. In the regression equation, the letter b represents the
constant/coefficient
and the letter a represents the
constant/coefficient
.
60 Ch. 8: Correlation
9.11. The dependent variable can be predicted more accurately as the correlation between the independent and dependent variables
increases/decreases
.
9.12. As the correlation between the predictor and the criterion variable increases, the standard error of estimate (SE)
increases/decreases
.
9.13. The predicted Y scores are expected to be
on/around
the regression line.
9.14. The criterion is predicted more accurately when SE is
larger/smaller
.
Answer/compute the following questions:
9.15. Study the following graph. If a company is able to maintain a 25% gross margin (the predictor X), what is the company’s predicted Return on Investment (ROI) (the criterion Y)?
9.16. Compute SE (the standard error of estimate) when the standard deviation of the Y-variable is 5 (SDY=5) and the correlation is 0.00 (r=0.00). Use the following equation to compute the SE:
What is the relationship between the SE (the standard error of estimate) and the SD of the dependent variable Y (SDY=5) when the correlation is zero (r=.00)? Explain.
9.17. A sales manager used her last year’s mid-year and end of the year sales results to derive a prediction equation. This year her sales force has the same 6 salespeople as last year and the market conditions are very similar to last year. In the middle of this year the manager wants to predict the year-end sales results for each of her 6 salespeople. Following are the mid-year sales results of the 6 salespeople, and the prediction equation.
a. Calculate the salespeople’s’ predicted end of the year sales results (Y’ scores). (Note: Use the prediction equation to compute the students’ Y’ scores.)
Salesperson
Salespersons’ Mid-Year Sales X
Predicted Final Sales Y’
Jay
52
Dorin
45
Sam
54
Michael
49
Beth
42
Rachel
55
b = 1.5 a = 13.2
9.18. Study the following graph, and determine what is the value of the slope of the regression line (i.e., b). Explain your answer.
9.19. Draw a regression line in the following graph, when the intercept is 10 (a=10), the mean of the X-variable is 20 (=20), and the mean of the Y-variable is 30 (=30).
9.20. Figure A shows three predictors, X1, X2, and X3, and their correlations with the criterion variable Y1. Figure B shows three predictors, Z1, Z2, and Z3, and their correlations with a criterion variable Y2.
a. Which predictor variables, those depicted in Figure A or those depicted in Figures B, correlate higher with each other?
b. Which set of three predictors, those shown in Figure A (X1, X2, and X3) or those shown in Figure B (Z1, Z2, and Z3) is likely to predict the criterion variables (Y1 or Y2) more accurately?
Figure A Figure B
=
–
=
2
1
r
SD
S
Y
E
a
X
b
Y
+
=
)
(
‘
Assignment 4
Chapter 10
10.1. In a t test for a single sample, the sample’s mean is compared to the population .
10.2. When we use a paired-samples t test to compare the pretest and posttest scores for a group of 45 people, the degrees of freedom (
d
f
) are _____.
10.3. If we conduct 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 the effect of college education on people’s earning by comparing the annual salaries of a randomly-selected group of 100 college graduates to the annual salaries of 100 randomly-selected group of people whose highest level of education is high school. To compare the mean annual salaries of the two groups, the researcher should use a t test for ______.
10.5. A training coordinator wants to determine the effectiveness of a program that makes extensive use of educational technology when training new employees. She compares the scores of her new employees who completed the training on a nationally-normed test to the mean score of all those in the country who took the same test. The appropriate statistical 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 questionnaire, 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 two forms.
Circle the
correct
answer:
10.7. A difference of 4 points between two homogeneous group
s is likely to be more/less statistically significant than the same difference (of 4 points) between two heterogeneous groups, when all four groups are taking completing the same survey and have approximately the same number of subjects.
a.
10.8. A difference of 3 points on a 100-item test taken by two groups is likely to be more/less statistically significant than a difference of 3 points on a 30-item test taken by the same 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 s
ame as
/different than
the number of post-test scores.
10.10. When we want to compare whether females’ scores on the GMAT are different from males’ scores, we should use a t test for paired
samples/inde
pende
n
t samples
.
10.11 In studies where the alternative (research) hypothesis is directiona
l
, the critical values for a one tail
ed
test/two-tailed test
should be used to determine the level of significance (i.e., the p value).
10.12 When the alternative hypothesis is: HA: u1=u2, the critical values for one
tailed
test/
two-tailed
test should be used to determine the level of statistical significance.
10.13. In a study conducted to compare the test scores of experimental and control groups, a 50-item test is administered to both groups at the end of the study. The mean of the experimental 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 compare the two means. The o
b
t
ain
ed t value is 1.89, and the p-value is .05. Can we conclude that the experimental treatment was c
l
ea
rl
y effective because the t value is s
ta
t
i
stic
all
y s
i
g
nifi
can
t
? Explain.
b.
10.14. Identify each of the following as a null hypothesis, a dir
ect
io
na
l 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 managers in their attitude toward the company. The CEO asks 30 randomly selected union members and 28 managers to complete a 40-item questionnaire designed to measure attitudes toward the company. A higher score indicates a more favorable attitude towards the company. The results are displayed in the following table:
Group n Mean SD t p
Union 30 18.30 9.85
.03
Managers 28 23.07 9.07
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 their attitudes towards the company again, using the same questionnaire as the one used the year before. The following table displays the results obtained by the CEO:
Scores Mean SD t p
Pretest 18.30 9.85
.0001
Posttest 22.10 1.26
c.
10.18. A plant manager randomly divides her employees into two groups. One group (Group A) includes 32 employees and the second one (Group B) includes 30 employees. After dividing the employees, the manager wants to confirm that the two groups are indeed similar in performance. He hypothesizes that there is no statistically significant difference between the two groups. To compare the two groups, the plant manager use ratings given by the employees’ front-line supervisors at the end of the previous year. The rating scale ranges from 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
n
Mean
SD
t
A
32
3.66
1.31
2.008
B
30
3.00
1.26
t crit(.05,df)=2.0;
t crit(.02,df)=2.390;
t crit(.01 ,df)=2.660
Which t test was used and why?
What were the degrees of freedom?
What are the manager’s conclusions? Explain.
10.19. Joe, a new manager suspects that the 23 new employees assigned to his department 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 assessment 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 social skills assessment 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 company. The results of the t test are:
Mean score= 635.13 SD= 71.53 t value= 3.75 p=.0001
a. Which t test is used and why?
b. What are the degrees of freedom (df)?
c. What are Joe’s conclusions? Explain
Chapter 11
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 (H
o
)
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
–
group
s sum of squares) and the SSg (betwee
n
–
groups
sum of squares) are equal to the sum 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 when 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 ho
mo
genous
/hetero
g
eneous
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
F
crit
(.
05
,
2
,2
0) = 3.49 and F
c
r
i
t
(
.
O
1
,2
,
20) = 5.85
a. Compute the obtained F ratio.
b. Determine whether the results are statistically significant.
c. 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 deviations obtained by the three age groups in each of the two regions:
Means
Standard Deviations
Ages
Ages
Ages
Ages
Ages
Ages
Region
18-25
26-35
36-45
18-25
26-35
36-45
Midwest
50.2
52.8
53.3
2.5
3.1
2.7
South
41.0
48.5
55.9
2.7
3.2
2.8
Two separate one-way ANOVA procedures are conducted to test 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 results 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 College B. Following are the means and standard deviations of the 3 classes in each of the two schools:
Means
Standard Dev
i
ations
SCHOOL
Stats
Stats
Stats
Stats
Stats
Stats
Class I
Class 2
Class 3
Class I
Class 2
Class 3
University A
71.4
78.8
90.2
3.2
4.3
4.8
College B
72.1
78.6
89.3
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<.0 5 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 no t attempt to compute the F ratios or the exact level of significanc e i n order to answer the questions below . ) Means of Means of Company Employees Using Employees Using Widget 1 Widget 2 Company A 55 53 Company B 50 48 Are there differences in questionnaire scores as a result of the using the two widgets? Explain. Are there differences in questionnaire scores between the two companies? Explain.
