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

35 5.1 5.8 6.5 6.1 5.1 5.5 5.3 5.5 6.9 5.0 4.9 6.0 4.8 6.1 5.65.1 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 4.94.8 5.9 5.1

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

38 1.6 1.8 1.4 1.5 1.5 1.6 1.4 1.1 1.2 1.4 1.7 1.0 1.7 1.9 1.61.4 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 1.51.6 1.4 1.3 1.7 1.5 1.6

(a) Use a calculator with mean and standard deviationkeys to calculate x1, s1, x2, and s2. (Round your answers to twodecimal places.)

x1 =

s1 =

x2 =

s2 =

(b) Let μ1 be the population mean for x1 and let μ2 bethe population mean for x2. Find a 99% confidence interval for μ1 −μ2. (Round your answers to two decimal places.)

lower limit

upper limit

(c) Explain what the confidence interval means in thecontext of this problem. Does the interval consist of numbers thatare all positive? all negative? of different signs? At the 99%level of confidence, is the population mean petal length ofIris virginica longer than that of Irissetosa?

Because the interval contains only positive numbers, we can saythat the mean petal length of Iris virginica islonger.

Because the interval contains only negative numbers, we can saythat the mean petal length of Iris virginica isshorter.   

Because the interval contains both positive and negativenumbers, we cannot say that the mean petal length of Irisvirginica is longer.

(d) Which distribution did you use? Why?

The Student's t-distribution was used becauseσ₁ and σ₂ are unknown.

The standard normal distribution was used because σ₁and σ₂ are unknown.

The Student's t-distribution was used becauseσ₁ and σ₂ are known.

The standard normal distribution was used because σ₁and σ₂ are known.

Do you need information about the petal lengthdistributions? Explain.

Both samples are large, so information about the distributionsis not needed

.Both samples are large, so information about the distributionsis needed.

Both samples are small, so information about the distributionsis needed.

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