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In: Statistics and Probability

Calculate true standard deviation of the diameter of a large batch of tires to a confidence...

Calculate true standard deviation of the diameter of a large batch of tires to a confidence level of 99% if the measured standard deviation in the diameter for a sample of 30 tires is 0.0795 cm.

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Expert Solution

Solution :  

Given that,

c = 99% = 0.99

s = 0.0795

n = 30

d.f. = n - 1 = 30 - 1 = 29

= 1 - 0.99 = 0.01

/ 2 = 0.005

1 - ( / 2) = 0.995

Now , using chi square table ,

= 0.025,29 = 52.335

=  0.975,26 = 13.121

The 99% confidence interval for is,

0.0795  [(30 - 1 ) / 52.335] < <  0.0795[(30 - 1 ) / 13.121]

0.059 < < 0.118

The 99% confidence interval for is ( 0.059 , 0.118 )

orchestra answered 2 years ago
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