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Bess [88]
3 years ago
14

Find the 90% confidence interval for the population standard deviation given the following.

Mathematics
1 answer:
lions [1.4K]3 years ago
5 0

Answer:

b. 2.01 < σ < 2.81

Step-by-step explanation:

The 90% confidence interval for the population standard deviation is calculated as:

\sqrt{\frac{(n-1)*s^{2} }{X^2_{\alpha/2 } } }    < σ < \sqrt{\frac{(n-1)*s^{2} }{X^2_{1-\alpha/2 } } }

Where n is equal to 51, s is equal to 2.34, \alpha is 10%, X^{2} _{\alpha /2} is the value for the Chi squared distribution with n-1 degrees of freedom that has a probability of \alpha /2 in the right tail and X^{2} _{1-\alpha /2} is the value for the Chi squared distribution with n-1 degrees of freedom that has a probability of 1-\alpha /2 in the right tail.

So, replacing n by 51, s by 2.34, X^{2} _{\alpha /2} by 67.50 and X^{2} _{1-\alpha /2} by 34.76, we get that the The 90% confidence interval is equal to:

\sqrt{\frac{(51-1)*2.34^{2} }{67.50} } } < σ <\sqrt{\frac{(51-1)*2.34^{2} }{34.76} } }

2.01 < σ < 2.81

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