The two companies manufacture a piece of plastic used in automobile production. This plastic piece is subject to wear during use. Therefore, it is desired to compare the amount of wear of plastic parts produced by the two companies. Each Friction wear was applied by taking random samples of 25 units from both companies and after 1000 cycles, wear amounts were observed. The average wear for the first company was 20mg / 1000 cycles and the standard deviation of wear was 1.5mg / 1000 cycles, the average for the second company was 12mg / 1000 cycles and the wear standard deviation was 1.8mg / 1000 cycles. It is assumed that the wear amount of both masses shows normal distribution with the same variance. a) For the difference between the average of wear amount

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
Topic Video
Question

The two companies manufacture a piece of plastic used in automobile production. This plastic piece is subject to wear during use. Therefore, it is desired to compare the amount of wear of plastic parts produced by the two companies. Each Friction wear was applied by taking random samples of 25 units from both companies and after 1000 cycles, wear amounts were observed. The average wear for the first company was 20mg / 1000 cycles and the standard deviation of wear was 1.5mg / 1000 cycles, the average for the second company was 12mg / 1000 cycles and the wear standard deviation was 1.8mg / 1000 cycles. It is assumed that the wear amount of both masses shows normal distribution with the same variance.
a) For the difference between the average of wear amount of plastic parts produced by the two companies, establish my confidence interval of 98%. Interpret the result. Can it be said that the amount of wear of the plastic material produced by the first company is higher?
b) For the average amount of wear of the plastic part produced by the second company, establish a 95% confidence interval. Interpret the result.

Expert Solution
Step 1

a)

 

Consider the pooled variance,

Statistics homework question answer, step 1, image 1

Step 2

Formula for confidence interval between two means:

Statistics homework question answer, step 2, image 1

The level of confidence is 0.98. Therefore, the level of significance is 1-0.98=0.02 and α/2=0.02/2=0.01. The degrees of freedom is 48.

From the t distribution table, the critical value corresponding with 48 degrees of freedom and 0.01 level of significance in “Area in one tail” is 2.4066.

Therefore,

Statistics homework question answer, step 2, image 2

Interpretation:

 

There is a 98% chance that the difference between the average of wear amount of plastic parts produced by the two companies is lies between 6.8722 and 9.1278.

 

Null hypothesis:

 

H0: The amount of wear of the plastic material produced by the first company is not higher than the second company.

 

Alternative hypothesis:

 

H1: The amount of wear of the plastic material produced by the first company is higher than the second company.

 

 

 

 

Rejection Rule based on Confidence interval:

 

  • If the hypothesized difference lies between the confidence limits, do not reject the null hypothesis.
  • If the hypothesized value lies outside the confidence limits, reject the null hypothesis.

 

Conclusion:

 

The hypothesized difference is 0.

The 98% confidence interval is (6.8722, 9.1278).

That is, the hypothesized difference does not lies between the limits.

From the rejection rule, reject the null hypothesis.

It can be concluded that the amount of wear of the plastic material produced by the first company is higher than the second company.

steps

Step by step

Solved in 3 steps with 4 images

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
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