The following data represent petal lengths (in cm) for independent random samples of two species of Iris.Petal length (in cm) ofIris virginica:x₁;n₁= 35

5.2, 5.7 ,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 6.4 5.3 5.5 6.7 5.7 4.9 4.8

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

1.6 1.7 1.4 1.5 1.5 1.6 1.4 1.1 1.2 1.4 1.7 1.0 1.7 1.9 1.6 1.4 1.5 1.4 1.2 1.3 1.5 1.3 1.6 1.9 1.4 1.6 1.5 1.4 1.6 1.2 1.9 1.5 1.6 1.4 1.3 1.7 1.5 1.7

(a) Use a calculator with mean and standard deviation keys to calculatex₁,s₁,x₂, ands₂. (Round your answers to two decimal places.)

x₁=

s₁=

x₂=

s₂=

(b) Let₁be the population mean forx₁and let₂be the population mean forx₂. Find a 99% confidence interval for₁₂.(Round your answers to two decimal places.)

lower limit

upper limit

(c) 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 ofIris virginicalonger than that ofIris setosa?

Because the interval contains only positive numbers, we can say that the mean petal length ofIris virginicais longer.

Because the interval contains only negative numbers, we can say that the mean petal length ofIris virginicais shorter.

Because the interval contains both positive and negative numbers, we cannot say that the mean petal length ofIris virginicais longer.

(d) Which distribution did you use? Why?

The Student'st-distribution was used because₁and₂are unknown.

The Student'st-distribution was used because₁and₂are known.

The standard normal distribution was used because₁and₂are unknown.

The standard normal distribution was used because₁and₂are known.

Do you need information about the petal length distributions? Explain.

Both samples are large, so information about the distributions is needed.

Both samples are small, so information about the distributions is not needed.

Both samples are small, so information about the distributions is needed.

Both samples are large, so information about the distributions is not needed.