A tyre manufacturer is considering a new designed treat pattern for its all-weat

Question

A tyre manufacturer is considering a new designed treat pattern for its all-weather tyres. Tests have indicated that these tyres provide better fuel economy and long tread life. The last remaining test is to measure the distance that it takes for a car to stop from 100km/h. They hope that the tyre will stop within 125 feet and will adopt the new tread pattern unless there is strong evidence that the tyres do not meet this objective. The distances (in feet) for 10 stops on a test track are 129, 128, 130, 132, 135, 123, 102, 125, 128 and 130. Should the company adopt the new tread pattern? Test an appropriate hypothesis and state your conclusion. Explain how you dealt with the outlier, and why you made the recommendation you did.

Explanation / Answer

Hypothesis testing is H0: mu=125 vs H1: mu<125

For the given data using online calculator we find n=10, mean=126.2 and sd=9.1384

Here we will use t distribution as n is small

t=(x-mu)/(sd/sqrt(n)=(126.2-125)/(9.1384/sqrt(10))=0.4153

Now we will find p value P(T<0.4153) for 10-1 df is 0.6562

Here p value is greater than usual level of significance i.e. 0.05 or 0.01 so we cannot reject null hypothesis.

Thus the company should not adopt the new trend.

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