# variance analysis

## Project Description:

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

a. compute the obtained f ratio.
b. 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. 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 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 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 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.
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