The following data represent petal lengths (in cm) for independent random samples of two species of iris (Reference: E. Anderson, Bulletin American Iris Society). Note: These data are also available for download at the Companion Sites for this text.

Petal length (in cm) of Iris virginica: x₁; n₁ = 35

Petal length (in cm) of Iris setosa: x₂; n₂ = 38

(a) Use a calculator with mean and standard deviation keys to verify that x̅₁ » 5.48, s₁ » 0.55, x̅₂ » 1.49, and s₂ » 0.21.

(b) Let m₁ be the population mean for x₁ and let m₂ be the population mean for x₂. Find a 99% con­fidence interval for m₁ – m₂.

(c) Interpretation Explain what the con­fidence interval means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 99% level of con­fidence, is the population mean petal length of Iris virginica longer than that of Iris setosa’.

(d) Check Requirements Which distribution (standard normal or Student’s t) did you use? Why? Do you need information about the petal length distributions? Explain.

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1 5.8 6.3 6.1 5.1 5.5 5.3 5.5 6.9 5.0 4.9 6.0 4.8 6.1 5.6 5.1 5.6 4.8 5.4 5.1 5.1 5.9 5.2 5.7 5.4 4.5 6.1 5.3 5.5 6.7 5.7 49 4.8 5.8 5.1 5 1.7 14 1.5 1.5 1.6 1.4 1.1 1.2 14 1.7 1.0 1.7 19 1.6 14 5 1.4 1.2 1.3 1.5 1.3 1.6 19 14 1.6 1.5 1.4 1.6 1.2 1.9 1.5 1.6 14 1.3 1.7 1.5 1.7