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It is given that a sample of 12 voltage levels of smartphone batteries comes from a population that is normally distributed. A 95% confidence interval is to be constructed to estimate the standard deviation of voltage levels.

A strict requirement to compute the confidence interval estimate of $蟽$using the${蠂}^2$distribution is that the sample should be selected from a normally distributed population (even if the sample size is large).

As the sample of voltage levels does not come from a population that is normally distributed, the 95% confidence interval to estimate $蟽$cannot be computed using the ${蠂}^2$distribution.

An alternate method that can be used to compute the confidence interval is discussed below:

• Obtain a set of 1000 or more bootstrap samples of size n=12 from the given sample.
• A bootstrap sample is a random sample obtained with the replacement of values from the given sample.
• Compute the sample standard deviation for each of the bootstrap samples.

$P_{\frac{伪}{2}脳100}<蟽<P_{1-\frac{伪}{2}脳100}=P_{\frac{0.05}{2}脳100}<蟽<P_{1-\frac{0.05}{2}脳100}$

Thus, the limits are obtained as follows:

$P_{2.5}<蟽<P_{97.5}$