Two students want to determine whose paper airplane model can fly the farthest. To put their models to the test, they recruit five friends to participate in a study. Because the friends have varying throwing abilities, the students decide to have each friend throw each model of airplane. To determine which paper airplane each friend throws first, a coin is tossed. The data are displayed in the table, which shows how far each airplane flies to the nearest inch. A 3-column table with 5 rows. Column 1 is labeled Friend with entries 1, 2, 3, 4, 5. Column 2 is labeled Model A with entries 150, 143, 108, 145, 128. Column 3 is labeled Model B with entries 228, 123, 212, 137, 174. The mean of the differences is 40 inches, and the standard deviation of the differences is 53.57 inches. The conditions for inference are met. A 90% confidence interval for the mean difference (B – A) in flight distance is –11.08 inches to 91.08 inches. What is the correct interpretation of this interval? The model B plane will fly farther than the model A plane 90% of the time. The model A plane will fly farther than the model B plane 90% of the time. The students can be 90% confident that, on average, the model A plane flies between 91.08 inches farther than and 11.08 inches less than the model B plane. The students can be 90% confident that, on average, the model B plane flies between 91.08 inches farther than and 11.08 inches less than the model A plane.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Two students want to determine whose paper airplane model can fly the farthest. To put their models to the test, they recruit five friends to participate in a study. Because the friends have varying throwing abilities, the students decide to have each friend throw each model of airplane. To determine which paper airplane each friend throws first, a coin is tossed. The data are displayed in the table, which shows how far each airplane flies to the nearest inch. A 3-column table with 5 rows. Column 1 is labeled Friend with entries 1, 2, 3, 4, 5. Column 2 is labeled Model A with entries 150, 143, 108, 145, 128. Column 3 is labeled Model B with entries 228, 123, 212, 137, 174. The mean of the differences is 40 inches, and the standard deviation of the differences is 53.57 inches. The conditions for inference are met. A 90% confidence interval for the mean difference (B – A) in flight distance is –11.08 inches to 91.08 inches. What is the correct interpretation of this interval? The model B plane will fly farther than the model A plane 90% of the time. The model A plane will fly farther than the model B plane 90% of the time. The students can be 90% confident that, on average, the model A plane flies between 91.08 inches farther than and 11.08 inches less than the model B plane. The students can be 90% confident that, on average, the model B plane flies between 91.08 inches farther than and 11.08 inches less than the model A plane.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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