Question

Cans of coke: Confidence interval if we use the data given in exercise 1, we get this 95% confidence interval estimate of the standard deviation of volumes with the new filling process: $0.1846<\sigma <0.4900$ oz. what does this confidence interval tell us about the new filling process?

Short answer

It is inferred that the actual value of standard deviation for volumes lies between the limits 0.1846 oz and 0.4900 oz, which is expressed at a 95% level of confidence.

Step-by-step solution

Step-1: Given information 

The confidence interval at 95% of the standard deviation of volumes with the new filling process: $0.1846<\sigma <0.4900$.

Step-2: Definition of the confidence interval

The confidence interval at a specific level of confidence is computed,

$\sqrt{\frac{\left(n-1\right)s^2}{{\chi }_R^2}}<\sigma <\sqrt{\frac{\left(n-1\right)s^2}{{\chi }_L^2}}$

It is inferred that the actual value of standard deviation for volumes lies between the limits$\sqrt{\frac{\left(n-1\right)s^2}{{\chi }_R^2}}$ and $\sqrt{\frac{\left(n-1\right)s^2}{{\chi }_L^2}}$, which is expressed with the certain level of confidence on which confidence interval is computed.

In this case, the two limits are 0.1846 oz and 0.4900 oz.

Thus, it can be expressed with 95% confidence that the actual value of standard deviation for volumes lies between the limits 0.1846 oz and 0.4900 oz.