20. Company records show that drivers get an average of 32,500 miles on a set of Road Hugger radial tires. Hoping to improve the average mileage, the company has added a new polymer to the rubber that should help protect the tires from deterioration. The hypotheses Ho : u = 32,500 and H1 : u> 32,500 are to be tested using a significance level a=0.05, where u is the average mileage on the new tires. (a) A random sample of 25 new tires shows an average of 33,800 miles with a standard deviation of 4,000 miles. Can the company conclude that the new polymer has significantly increased the average mileage of the tires? (You have to write down the decision rule, the test statistic and the conclusion). Solution: For a=0.05, reject H, if t > 1.711, accept Ho ift< 1.711 where t has 24 degrees of freedom. Orf- X 4000//25 33800 – 32500 Test statistic is t = = 1.625 which is less than 1.711. Accept Ho and conclude that sample evidence does not support that new polymer has significantly increased the average mileage of the tires. That is, the company cannot conclude that the new polymer has significantly increased the average mileage of the tires.
20. Company records show that drivers get an average of 32,500 miles on a set of Road Hugger radial tires. Hoping to improve the average mileage, the company has added a new polymer to the rubber that should help protect the tires from deterioration. The hypotheses Ho : u = 32,500 and H1 : u> 32,500 are to be tested using a significance level a=0.05, where u is the average mileage on the new tires. (a) A random sample of 25 new tires shows an average of 33,800 miles with a standard deviation of 4,000 miles. Can the company conclude that the new polymer has significantly increased the average mileage of the tires? (You have to write down the decision rule, the test statistic and the conclusion). Solution: For a=0.05, reject H, if t > 1.711, accept Ho ift< 1.711 where t has 24 degrees of freedom. Orf- X 4000//25 33800 – 32500 Test statistic is t = = 1.625 which is less than 1.711. Accept Ho and conclude that sample evidence does not support that new polymer has significantly increased the average mileage of the tires. That is, the company cannot conclude that the new polymer has significantly increased the average mileage of the tires.
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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Question
In this question, I don't understand how we got number 1.711 where I have highlighted. Please help me to explain. Thank you.
Transcribed Image Text:20.
Company records show that drivers get an average of 32,500 miles on a set of Road Hugger radial
tires. Hoping to improve the average mileage, the company has added a new polymer to the rubber
that should help protect the tires from deterioration.
The hypotheses Ho : u = 32,500 and
H : u > 32,500 are to be tested using a significance level a =0.05, where u is the average mileage
on the new tires.
(a)
A random sample of 25 new tires shows an average of 33,800 miles with a standard deviation of 4,000
miles. Can the company conclude that the new polymer has significantly increased the average
mileage of the tires? (You have to write down the decision rule, the test statistic and the conclusion).
Solution: For a=0.05, reject Ho if t> 1.711, accept Ho if t < 1.711 where t has 24 degrees of freedom.
33800 – 32500
Test statistic is t =
=1.625 which is less than 1.711.
S/Nn
4000//25
Accept Ho and conclude that sample evidence does not support that new polymer has significantly
increased the average mileage of the tires. That is, the company cannot conclude that the new polymer
has significantly increased the average mileage of the tires.
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