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19.Use the given degree of confidence and Sample data to find a confidence interval for the population standard deviation. Assume that the population has a normal distribution. Round the confidence interval limits to one more decimal place than is used for the original set of data.
The amounts (in ounces) of juice in eight randomly selected juice bottles are: 15.9, 15.2, 15.3, 15.2, 15.3, 15.8, 15.1, 15.2 find a 98% confidence interval for the population standard deviation
Please with explain how you get there

Respuesta :

Answer:

0.19 < σ < 0.72

Step-by-step explanation:

The sample standard deviation is 0.30.

The population variation can be estimated between:

(n−1) s² / χ²α/2 < σ² < (n−1) s² / χ²(1−α/2)

At 98% confidence and 7 degrees of freedom, χ²α/2 = 18.5 and χ²(1−α/2) = 1.24.

(8−1) 0.30² / 18.5 < σ² < (8−1) 0.30² / 1.24

0.034 < σ² < 0.512

0.19 < σ < 0.72