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# Introductory Statistics assignment

## Introductory Statistics Assignment #6

1. Lief Enterprises manufactures a variety of steel, plastic and ceramic components used in the automotive industry. Major products include brakes and clutches. Lief is considering changing the type of material used for the brake pads.

Ten shoes have been specially designed such that both the old material and the new material can be bonded to the shoe in alternating strips. The ten shoes are installed on ten different vehicles and driven for 10,000 km each. The percentage wear for each pad was measured (0% = new and 100% = completely worn away). The results are given below

Old 76 70 87 46 67 35 54 71 29 44
New 65 63 71 49 57 43 51 59 33 40

a) Lief will only switch materials if they can clearly show that the new material lasts longer (does not wear out as quickly). Test the appropriate hypotheses at α = 0.05. Use the Classical Approach.

Hypotheses in simple words
Null hypothesis:

Alternate hypothesis:

Hypotheses in symbols
Null hypothesis:

Alternate hypothesis:

Test statistic – what formula will you use?

Decision rule – when will you reject the null hypothesis?

Calculations:

Conclusion:

b) Suppose that Lief Enterprises uses the above methodology every time that it considers changing the material used in the brake pads. What proportion of the time will they switch materials when the new material is not superior to the old one? Explain.

c) Suppose that Lief did not use 10 shoes with alternating strips of material, but used 20 shoes, 10 with the new material and 10 with the old. The shoes were installed on 20 different vehicles and driven for 10,000 km each. Repeat the hypothesis test in (a) with this research design.

Hypotheses in simple words
Null hypothesis:

Alternate hypothesis:

Hypotheses in symbols
Null hypothesis:

Alternate hypothesis:

Test statistic – what formula will you use?

Decision rule – when will you reject the null hypothesis?

Calculations:

Conclusion:

d) Why is your conclusion different in (c) from the conclusion in (a)?

e) Explain what is meant by the conclusion “fail to reject H0”.

Last Updated on February 11, 2019

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