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In: Statistics and Probability

A random sample of 21 nickels in circulation were measured with a very accurate micrometer to...

A random sample of 21 nickels in circulation were measured with a very accurate micrometer to find a mean of 0.834343 inch and a standard deviation of 0.001886 inch.

What is a 99% confidence interval for the standard deviation (correct to 4 decimal places) of all circulating nickels?

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Expert Solution

Solution :

Given that,

s = 0.001886

s2 = 0.0434

n = 21

Degrees of freedom = df = n - 1 = 21 - 1 = 20

At 99% confidence level the 2 value is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

1 - / 2 = 1 - 0.005 = 0.995

2L = 2/2,df = 40

2R = 21 - /2,df = 7.432

The 99% confidence interval for is,

(n - 1)s2 / 2/2 < < (n - 1)s2 / 21 - /2

(20)(0.0434) / 40 < < (20)(0.0434) / 7.432

0.0217 < < 0.11679

0.1473 < < 0.3717

(0.1473 , 0.3417)

orchestra answered 1 year ago
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