Question

The following data represent petal lengths (in cm) for independent random samples of two species of Iris.

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

5.1	5.9	6.4	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	5.7	5.2

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

1.6	1.9	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	1.6

(a) Use a calculator with mean and standard deviation keys to calculate x₁, s₁, x₂, and s₂. (Round your answers to two decimal places.)

x1 =	1
s1 =	2
x2 =	3
s2 =	4

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

lower limit	5
upper limit	6

(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 of Iris virginica longer than that of Iris setosa?

Because the interval contains only positive numbers, we can say that the mean petal length of Iris virginica is longer. Because the interval contains only negative numbers, we can say that the mean petal length of Iris virginica is shorter.     Because the interval contains both positive and negative numbers, we cannot say that the mean petal length of Iris virginica is longer.

(d) Which distribution did you use? Why?

The Student's t-distribution was used because σ₁ and σ₂ are unknown. The standard normal distribution was used because σ₁ and σ₂ are unknown.     The standard normal distribution was used because σ₁ and σ₂ are known. The Student's t-distribution was used because σ₁ and σ₂ are 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 large, so information about the distributions is not needed.     Both samples are small, so information about the distributions is needed. Both samples are small, so information about the distri

Answer 1

(a)

1	5.4914
s1	0.5680
2	1.4947
s2	0.2155

(b)

= 0.01

ndf = 35 + 38 - 2= 71

From Table, critical values of t = 2.6469

Lower limit = (5.4914 - 1.4947) - (2.6469 X 0.0990) = 3.9967 - 0.2620 = 3.7347

Upper limit = (5.4914 - 1.4947) + (2.6469 X 0.0990) = 3.9967 + 0.2620 = 4.2587

So, we get:

Lower limit	3.7347
Upper limit	4.2587

(c)

Correct option:

Because the interval contains only positive values we can say that the mean petal length of Iris Virginea is longer.

(d) Correct option:

The Student's t distribution was used because and are unknown.

Correct option:

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