Aresearch engineer for a tire manufacturer is investigating tire life for a new rubber compound. she has built 10 tires and tested them to end-of-life in a road test. the sample mean and standard deviation are 61,492 and 2990 kilometers, respectively. assume population is approximately normally distributed. (a) can you conclude, using =0.05, that the standard deviation of tire life exceeds 3000 km ? yes ot no ?

The standard deviation of tire life does exceed 3000 km

Step-by-step explanation:

This is a Chi-Square Hypothesis Test for the Standard Deviation, here we have

so, this is an upper one-tailed test.

The test statistic is

where

n = 10 is the sample size

s = sample standard deviation

= population standard deviation

we would reject the null hypothesis if

where

is the critical value corresponding to the level of significance with n-1 degrees of freedom.

we can use either a table or a spreadsheet to compute this value.

In Excel use

CHISQ.INV(0.05,9)

In OpenOffice Calc use

CHISQINV(0.05;9)

and we get this value equals 3.3251

Working out our T statistic

Since T > 3.3251 we reject the null and conclude that the standard deviation of tire life exceeds 3000 km.

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step-by-step explanation:

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