The following data represent petal lengths (in cm) for independent random samples of two species of Iris.
Petal length (in cm) of Iris virginica: x_{1}; n_{1} = 35
5.0 | 5.9 | 6.5 | 6.1 | 5.1 | 5.5 | 5.3 | 5.5 | 6.9 | 5.0 | 4.9 | 6.0 | 4.8 | 6.1 | 5.6 | 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 | 5.9 | 5.3 |
Petal length (in cm) of Iris setosa: x_{2}; n_{2} = 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 | 1.6 | 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 |
Let μ_{1} be the population mean for x_{1} and let μ_{2} be the population mean for x_{2}. Find a 99% confidence interval for μ_{1} − μ_{2}. (Round your answers to two decimal places.)
lower limit | ? |
upper limit | ? |
The following data represent petal lengths (in cm) for independent random samples of two species of Iris.
5.3 | 5.7 | 6.2 | 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 | 5.9 | 5.1 |
1.5 | 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 | 1.6 |
x_{1} = | |
s_{1} = | |
x_{2} = | |
s_{2} = |
(b) Let μ_{1} be the population mean for x_{1} and let μ_{2} be the population mean for x_{2}. Find a 99% confidence interval for μ_{1} − μ_{2}. (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 of Iris virginica longer than that of Iris setosa?
(d) Which distribution did you use? Why?
Petal length (in cm) of Iris virginica: x_{1}; n_{1} = 36
5.2 | 5.6 | 6.1 | 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 | 5.8 | 5.2 | 5.2 |
Petal length (in cm) of Iris setosa: x_{2}; n_{2} = 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 | 1.6 | 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 | 1.5 |
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