The life-time of a tire is known to be normally distributed with the mean 60,000

Question

The life-time of a tire is known to be normally distributed with the mean 60,000 km and standard deviation 150. A research engineer for a tire manufacturer has built 25 tires with a few rubber compound and obtained the mean life-time 60, 075 km of 25 tires. The engineer would like to demonstrate that the mean life of this new tire exceeds 60,000 kilometers State the null and the alternative hypothesis to be tested in this case. Test the hypotheses in 1) using acceptance region approach with 5% significance level (your acceptance region will be calculated from the significance level).

Explanation / Answer

This is a question of testing of hypothesis at 5% significance level.

a) Set up hypotheses as:

H0: mu = Mean life of new tyres = 60000

Ha: Mu >60000

(Right tailed test)

b) Population std dev = sigma = 150

Sample mean x bar = 60075

Sample size n = 25

Hence Std error of sample = sigma/rtn = 150/5

= 30

Since sample size <30, we can use t test though we know sigma

t = Test statistic = (x bar-mu)/STd error = 75/30 = 2.5

df = 25-1 =24

p value = 0.009827

p < 0.05 our significant level

Hence we can reject null hypothesis

Conclusion:

Accept the claim that life of mean tyres exceed 60000

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