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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 (df) 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 researchershould 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 appropriatestatistical 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 groups is likely to be more/lessstatistically significant than thesame 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.
10.8. A difference of 3 points on a 100-item test taken by two groups is likely to be more/lessstatistically 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 same 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/independent samples.
10.11 In studies where the alternative (research) hypothesis is directional, the critical values for a one tailed test/two-tailed testshould 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 obtained t value is 1.89, and the p-value is .05. Can we conclude that the experimental treatment wasclearly effective because the t value is statistically significant? Explain.
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 scoresof 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:
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 implementingthe programs for a year, the CEO asks the same group of union members (n=30) to about their attitudes towards the company again, using the same questionnaire as the one used the year before. The following table displays the resultsobtained 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) includes 32 employees and thesecond 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 asfollows:
|
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
|
||
- 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 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 allprospective employees a social skills assessment before being hired. The mean score obtained by Joe‘s new employees is635.13 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= 635.13SD= 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 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 homogenous/heterogeneousin 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 standarddeviations 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: Theone 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 Deviations
|
|||||
|
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 ineach 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
|
Means of
|
|
|
Company
|
Employees Using
|
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.
