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a manufacture of 10cm ball bearings claims the standard deviation of it's bearings diameter is less...

a manufacture of 10cm ball bearings claims the standard deviation of it's bearings diameter is less than 0.21. A random sample of 12 bearings found the standard deviation of the diameter to be 0.14cm. is there enough evidence , at the 0.01 level of significance to back up the manufactures claim?

Math   Statistics-And-Probability   
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Answer #1

H0: = 0.21

Ha: < 0.21

Test statistics

= ( n - 1 ) S2 / 2

= (12 - 1) * 0.142 / 0.212

= 4.89

Critical value at 0.01 significance level with 11 df = 3.053

Since test statistics > 3.053

Do not reject the null hypothesis.

We do not have suffcient evidence to support the claim that the standard deviation of it's bearings diameter is less than 0.21.

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