Question: Botany: Iris. The following data represent petal lengths (in cm) for independent random samples of two species of iris (Reference: E. Anderson, Bulletin American Iris Society).

Petal length (in cm) of iris virginica: \(x_{1} ; n_{1}=35\)

Petal length (in cm) of iris setosa: \({{x}_{2}};{{n}_{2}}=38\)

1. Use a calculator with mean and standard deviation keys to verify that \(\bar{x}_{1} \approx 5.48, s_{1} \approx 0.55, \bar{x}_{2} \approx 1.49\), and \(s_{2} \approx 0.21\)
2. Let \(\mu_{1}\) be the population mean for \(x_{1}\) and let \(\mu_{2}\) be the population mean for \(x_{2}\). Find a \(99 \%\) confidence interval for \(\mu_{1}-\mu_{2}\).
3. 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?
4. Which distribution (standard normal or Student's \(t\) ) did you use? Why? do we need information about the petal length distributions? Explain.

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