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10.1. In a ttest for a single sample, the sample’s mean is compared to the population .
10.2. When we use a paired-samples ttest 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 ttest 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 ttest 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 ttest 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 groupsis likely to be more/lessstatistically significant than the same difference (of 4 points) between two heterogeneousgroups, 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 ttest for paired samples is used to compare the pretest and the posttest means, the number of pretest scores is the same as/different thanthe 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 ttest 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 pvalue).
10.12 When the alternative hypothesis is: HA: u1=u2,the critical values for one tailed test/two-tailed testshould be used to determine the level of statistical significance.
10.13. Ina 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 ttest for independent samples to compare the two means. The obtained tvalue is 1.89, and the p-value is .05. Can we conclude that the experimental treatment was clearly effectivebecause the tvalue is statistically significant?Explain.
10.14. Identify each of the following as a nullhypothesis, a directionalhypothesis, or a non-directionalhypothesis.
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 ttest 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 ttest 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=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 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) 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 ttest 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
tcrit(.05,df)=2.0;
t crit(.02,df)=2.390;
t crit(.01,df)=2.660
a.Which ttest 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 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 ttest 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 ttest are:
Mean score= 635.13SD= 71.53t value= 3.75 p=.0001
d.
Which ttest is used and why?
What are the degrees of freedom (df)?
What are Joe’s conclusions? Explain
11.1. While a ttest is used to compare twomeans, the one-way ANOVA can be used to simultaneously compare ____ groups.
11.2. An ANOV A is considered to be an extension of the ttest 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 ttests 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) inANOVA is: __________.
11.7. The total(or grand)mean in ANOV A can be thought of as the mean of ____.
11.8. The SSw (within-groupssum 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 Fratio, 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 Fratio is/is notstatistically significant.
11.14. The Fratio is likely to be statistically significant when the differences between
the group means are small/large. .
11.15. The Fratio 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 valuesfor the Fratio at p=.05and p=.01
Fcrit(.05,2,20)= 3.49 and Fcrit(.O1,2,20)= 5.85
Compute the obtained Fratio.
Determine whether the results are statistically significant.
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. Estimatewhich Fratio 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 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. Estimatewhich Fratio 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 Fratios are computed. Estimate which of the two Fratios is likely to be higher and explain your answer.
11.20. In a study comparing means of 4 groups, the Fratio was significant at the p5level. 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 obtainedHSD value at the p=.05level 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 notattempt 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.