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 oneway 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 oneway 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–groups sum of squares) and the SSg (between–groups
sum of squares) are equal to thesum of squares.
11.9. To find the MS_{g}, 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
F_{crit}(.05,2,20) = 3.49 and F_{c}_{r}_{i}_{t}(.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 1825, 2635, 3645) 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 
1825 
2635 
3645 
1825 
2635 
3645 
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 oneway 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 oneway 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 oneway 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 statisticallydiffer 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 pilottest 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.