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 =

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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 = 

 

STATE: Ethan Temeles of Amherst College, with his colleague W. John Kress, stud-
ied 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 form of the humming-
birds' beaks have evolved to match each other. If that is true, flower varieties fertilized
by different hummingbird species should have distinct distributions of length.
Table 25.1 gives length measurements (in millimeters) for samples of three varieties
of Heliconia, each fertilized by a different species of hummingbird. Do the three varieties
display distinct distributions of length? In particular, are the average lengths of their
flowers different? perform an ANOVA rest, explaining every
Estep.
TABLE 25.1
47.12
48.07
41.90
39.63
.38.10
Flower lengths (millimeters) for three Heliconia varieties
H. bihai
46.75 46.81 47.12 46.67
48.34 48.15
50.26 50.12
H. caribaea red
42.01 41.93
43.09 41.47
40.66 37.87 39.16
42.18
37.97 38.79 38.23 38.87
47.43 46.44 46.64
46.34 46.94 48.36
41.69 39.78 40.57
37.40 38.20 38.07
37.78 38.01
H. caribaea yellow
36.11 36.03 35.45
36.78 37.02 36.52
35.17 36.82 36.66 35.68 36.03 34.57
38.13 37.10
34.63
Transcribed Image Text:STATE: Ethan Temeles of Amherst College, with his colleague W. John Kress, stud- ied 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 form of the humming- birds' beaks have evolved to match each other. If that is true, flower varieties fertilized by different hummingbird species should have distinct distributions of length. Table 25.1 gives length measurements (in millimeters) for samples of three varieties of Heliconia, each fertilized by a different species of hummingbird. Do the three varieties display distinct distributions of length? In particular, are the average lengths of their flowers different? perform an ANOVA rest, explaining every Estep. TABLE 25.1 47.12 48.07 41.90 39.63 .38.10 Flower lengths (millimeters) for three Heliconia varieties H. bihai 46.75 46.81 47.12 46.67 48.34 48.15 50.26 50.12 H. caribaea red 42.01 41.93 43.09 41.47 40.66 37.87 39.16 42.18 37.97 38.79 38.23 38.87 47.43 46.44 46.64 46.34 46.94 48.36 41.69 39.78 40.57 37.40 38.20 38.07 37.78 38.01 H. caribaea yellow 36.11 36.03 35.45 36.78 37.02 36.52 35.17 36.82 36.66 35.68 36.03 34.57 38.13 37.10 34.63
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