Chapter 5, Problem 028 Your answer is partially correct. Try again. Two companie

Question

Chapter 5, Problem 028 Your answer is partially correct. Try again. Two companies manufacture a rubber material intended for use in an automotive application. The part will be subjected to abrasive wear in the field application, so we decide to compare the material produced by each company in a test. Twenty-five samples of material from each company are tested in an abrasion test, and the amount of wear after 1000 cycles is observed. For company 1, the sample mean and standard deviation of wear are 1-21 milligrams/1000 cycles and s1 = 3 milligrams/1000 cycles, while for company 2 they are 12-13 milligrams/1000 cycles and s2-7 milligrams/1000 cycles. Use = 0.05 and assume each population is normally distributed but that their variances are not (a) Test the hypothesis Ho: 1 = 2 verses H1: 1 2 Round your answer to two decimal places (e.g. 98.76) Calculate to (b) Do the data support the claim that the two companies produce material with different mean wear? yes (c) Do the data support a claim that the material from company 1 has higher mean wear than the material from company 27yes the absolute tolerance is +/-0.01

Explanation / Answer

The statistical software output for this problem is:

Two sample T summary hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 0
(without pooled variances)

Hypothesis test results:

Hence,

t0 = 5.25

Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 8 1.5231546 32.528606 5.2522573 <0.0001

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