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...

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.

H
₀: Median for additive 1 − Median for additive 2 ≤ 0

H
_a: Median for additive 1 − Median for additive 2 > 0H
₀: Median for additive 1 − Median for additive 2 ≠ 0

H
_a: Median for additive 1 − Median for additive 2 = 0H
₀: Median for additive 1 − Median for additive 2 ≥ 0

H
_a: Median for additive 1 − Median for additive 2 <>H
₀: Median for additive 1 − Median for additive 2 = 0

H
_a: Median for additive 1 − Median for additive 2 ≠ 0H
₀: 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 thep-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Jun 10, 2022

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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...

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