Ethan Temeles and W. John Kress of Amherst College studied the relationship between varieties of the tropical flower Heliconia on the island of Dominica and the different species of hummingbirds that fertilize the flowers. Over time, the researchers believe, the lengths of the flowers and the forms of the hummingbirds' beaks have evolved to match each other. If that is true, flower varieties fertilized by different hummingbird species should have distinct distributions of length. The table gives length measurements (in millimeters) for samples of three varieties of Heliconia, each fertilized by a different species of hummingbird. Using the data from the table, the ANOVA F-test gives a P-value<0.0001 and the test statistic F=259.12. The very small P-value gives good reason to conclude that the three varieties of flowers have different mean lengths. Does the mean length for the H. bihai flower differ significantly from the mean length of the H. caribaea red or the H. caribaea yellow flower, and does the mean length for the H. caribaea red flower differ significantly from the H. caribaea yellow flower? Flower lengths (millimeters) for three varieties - We want to be 90% confident that we do not wrongly reject any of the three null hypotheses. Tukey pairwise comparisons can give conclusions that meet this condition. - Use the technology of your choice to find the upper and lower limits of the Tukey simultaneous u1−u2 confidence interval. Give your answers to two decimal places. (u1-u2) lower = (u1-u2) upper = Use the technology of your choice to find the upper and lower limits of the Tukey simultaneous u1−u3 confidence interval. Give your answers to two decimal places. (u1-u3) lower = (u1-u3) upper = Use the technology of your choice to find the upper and lower limits of the Tukey simultaneous u2−u3 confidence interval. Give your answers to two decimal places. (u2-u3) lower = (u2-u3) upper =
Ethan Temeles and W. John Kress of Amherst College studied the relationship between varieties of the tropical flower Heliconia on the island of Dominica and the different species of hummingbirds that fertilize the flowers. Over time, the researchers believe, the lengths of the flowers and the forms of the hummingbirds' beaks have evolved to match each other. If that is true, flower varieties fertilized by different hummingbird species should have distinct distributions of length.
The table gives length measurements (in millimeters) for samples of three varieties of Heliconia, each fertilized by a different species of hummingbird. Using the data from the table, the ANOVA F-test gives a P-value<0.0001 and the test statistic F=259.12. The very small P-value gives good reason to conclude that the three varieties of flowers have different
Flower lengths (millimeters) for three varieties
- We want to be 90% confident that we do not wrongly reject any of the three null hypotheses. Tukey pairwise comparisons can give conclusions that meet this condition.
- Use the technology of your choice to find the upper and lower limits of the Tukey simultaneous u1−u2 confidence interval. Give your answers to two decimal places.
(u1-u2) lower =
(u1-u2) upper =
Use the technology of your choice to find the upper and lower limits of the Tukey simultaneous u1−u3 confidence interval. Give your answers to two decimal places.
(u1-u3) lower =
(u1-u3) upper =
Use the technology of your choice to find the upper and lower limits of the Tukey simultaneous u2−u3 confidence interval. Give your answers to two decimal places.
(u2-u3) lower =
(u2-u3) upper =
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