## Related questions with answers

Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5.

Why might finding a bootstrap confidence interval not be a good idea for these data?

Solution

VerifiedGiven:

$\begin{align*} n&=\text{Sample size}=6 \\ c&=\text{Confidence level}=95\%=0.95 \end{align*}$

A bootstrap sample is a smaller sample that is taken from a larger sample.

Since the given sample has only 6 data values, the sample is small and thus we shouldn't take even smaller samples of this sample.

If we would take smaller samples of this sample, then we would repeatedly get the same samples (as there are at most 20 distinct samples of $k$ of the 6 data values, where $k$ is an integer from 1 to 5) and thus it would be better to list all samples and observe their means instead of taking bootstrap samples.

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