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
icon
Related questions
Question
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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman