10. [-/4.42 Points] DETAILS BBUNDERSTAT12 7.4.016.MIS. MY NOTES ASK YOUR TEACHER 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; nj = 36 5.2 5.8 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 5.9 5.2 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 14 1.7 1.0 1.7 1.9 1.6 14 1.5 1.4 1.2 13 1.5 13 16 19 14 16 15 14 16 12 1.9 1.5 1.4 1.3 1.7 1.5 1.7 A USE SALT (a) Use a calculator with mean and standard deviation keys to calculate x1, $1, x2, and $2. (Round your answers to four decimal places.) X1 (b) Let pj be the population mean for x 1 and let #2 be the population mean for x2. Find a 99% confidence interval for #1 - #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? Because the Interval contains only positive numbers, we can say that the mean petal length of Iris virginica is longer. Because the Interval contains ers, 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-d because #1 and 62 are known. The Stud e 1 and d2 are unknown. The standard normal distribution was used because s , and 62 are known. The standard normal distribution was used because s, and ez are unknown. Do you need information about the petal length distributions? Explain. Both samples are small, so inform Both samples are large, so In Both samples are small, so Infor distributions is not needed Both sam butions is not needed. DII FB C @ 6 del W