When the null hypothesis for an ANOVA analysis comparing four treatment means is rejected, two comparisons of treatment means can be made four comparisons of treatment means can be made six comparisons of treatment means can be made eight comparisons of treatment means can be made

A new approach for teaching mathematics was introduced that engages students in group investigations and mathematical modeling. After field tests in 36 high schools over a​ three-year period, researchers compared the performances the new approach students with those taught using a traditional curriculum. During the​ study, students in both classes that used the new approach and traditional classes took a Algebra test that did not allow them to use calculators. The accompanying table shows the results. Are the mean scores of the two groups significantly​ different?  Write appropriate hypotheses. Let μN be the mean Algebra test score for students in classes that use the new approach. Let μT  be the mean Algebra test score for students in traditional classes.  ​b) Do you think the assumptions for inferences are​ satisfied? Explain.     A. No. The students within each class are not independent individuals as their score on the Algebra test is dependent upon other students in the…

Parents of teenage boys often complain that auto insurance costs more, on average, forteenage boys than for teenage girls. A group of concerned parents examines a randomsample of insurance bills. The mean annual cost for 36 teenage boys was $679. For 23teenage girls, it was $559. From past years, it is known that the population standarddeviation for each group is $180. Determine whether or not you believe that the mean costfor auto insurance for teenage boys is greater than that for teenage girls. Test at the 5% levelof significance.

A researcher wanted to find the best viewing distance for watching a TV screen. He recruited the following number of participants and asked them to evaluate their satisfaction of the viewing distance. Then, he conducted an ANOVA to see if there is any significant mean differences. Here are the number of participants by each group: Group 1 (4 feet) - 5 people Group 2 (7 feet) - 5 people Group 3 (10 feet) - 6 people Group 4 (13 feet) - 5 people Group 5 (16 feet) - 4 people Given the numbers as presented above, what is the degrees of freedom for within groups for this analysis? a. 4 b. 20 O c. 21 d. 25