A research engineer for a tire manufacturer is investigating tire life for a new

Question

A research engineer for a tire manufacturer is investigating tire life for a new rubber compound and has built 16 tires and tested them to end-of-life in a road test. The sample mean and standard deviation are 60, 139.7 and 3712.32 kilometers. Can you conclude, using alpha = 0.05, 0.05, that the standard deviation of tire life is less than 4000 kilometers? There sufficient evidence to indicate the true standard deviation of tire life is less than 4000 km at alpha = 0.05. State bounds for the P-value of this test. 0.1

Explanation / Answer

a)
H0 : sigma^2 = (4000)^2
Ha : sigma^2 < (4000)^2

we observe the variable
Chi^2(15) = ( n-1)*s^2 / sigma^2
= 15 * (3712.32)^2 / 4000^2
= 12.91

Formulating in terms of a confidence interval
P(chi^2(15 , 0.95) < ( n-1)*s^2 / sigma^2)

sigma^2 < (n-1) *s^2 / chi^2(15 , 0.95)
(4000)^2 < 15 * (3712.32)^2 / 7.261
16000000 < 28469879.73

Accept Ho
There is sufficient evidence to indicate that true standard deviation of tire life is less than 4000

b)

p value for chi square value = 12.91 with df = 15
p value = 0.6092

Here, we accept Ho because p value > 0.05

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