In this exercise involving paired differences, consider that it is reasonable to assume the populations being compared have approximately the same shape and that the distribution of paired differences is approximately symmetric. Two fuel additives are tested to determine their effect on miles per gallon for passenger cars. Suppose test results for 12 cars follow; each car was tested with both fuel additives. Additive Car 1 2 1 20.12 18.05 2 24.56 22.77 3 23.03 23.57 4 19.15 16.06 5 20.23 21.22 6 24.77 22.80 7 16.16 17.20 8 18.55 15.98 9 21.87 20.03 10 25.23 22.15 11 23.21 21.78 12 24.02 23.70 Use ? = 0.05 and the Wilcoxon signed-rank test to see whether there is a significant difference between the median miles per gallon for the additives. State the null and alternative hypotheses. H0: Median for additive 1 − Median for additive 2 ≤ 0 Ha: Median for additive 1 − Median for additive 2 > 0H0: Median for additive 1 − Median for additive 2 ≠ 0 Ha: Median for additive 1 − Median for additive 2 = 0 H0: Median for additive 1 − Median for additive 2 ≥ 0 Ha: Median for additive 1 − Median for additive 2 < 0H0: Median for additive 1 − Median for additive 2 = 0 Ha: Median for additive 1 − Median for additive 2 ≠ 0H0: Median for additive 1 − Median for additive 2 > 0 Ha: Median for additive 1 − Median for additive 2 = 0 Find the value of the test statistic. T + = Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion.

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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In this exercise involving paired differences, consider that it is reasonable to assume the populations being compared have approximately the same shape and that the distribution of paired differences is approximately symmetric.

Two fuel additives are tested to determine their effect on miles per gallon for passenger cars. Suppose test results for 12 cars follow; each car was tested with both fuel additives.

	Additive
Car	1	2
1	20.12	18.05
2	24.56	22.77
3	23.03	23.57
4	19.15	16.06
5	20.23	21.22
6	24.77	22.80
7	16.16	17.20
8	18.55	15.98
9	21.87	20.03
10	25.23	22.15
11	23.21	21.78
12	24.02	23.70

Use ? = 0.05 and the Wilcoxon signed-rank test to see whether there is a significant difference between the median miles per gallon for the additives.

State the null and alternative hypotheses.

H₀: Median for additive 1 − Median for additive 2 ≤ 0
H_a: Median for additive 1 − Median for additive 2 > 0H₀: Median for additive 1 − Median for additive 2 ≠ 0
H_a: Median for additive 1 − Median for additive 2 = 0 H₀: Median for additive 1 − Median for additive 2 ≥ 0
H_a: Median for additive 1 − Median for additive 2 < 0H₀: Median for additive 1 − Median for additive 2 = 0
H_a: Median for additive 1 − Median for additive 2 ≠ 0H₀: Median for additive 1 − Median for additive 2 > 0
H_a: Median for additive 1 − Median for additive 2 = 0

Find the value of the test statistic.

T⁺ =

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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