Is this statement true or false? 1. A 95% bootstrap confidence interval for x(pa

Question

Is this statement true or false?
1. A 95% bootstrap confidence interval for x(parameter) is always between zero and one (inclusive)
2. A 99% bootstrap confidence interval for x(parameter) is always between zero and one (inclusive)
Is this statement true or false?
1. A 95% bootstrap confidence interval for x(parameter) is always between zero and one (inclusive)
2. A 99% bootstrap confidence interval for x(parameter) is always between zero and one (inclusive)

1. A 95% bootstrap confidence interval for x(parameter) is always between zero and one (inclusive)
2. A 99% bootstrap confidence interval for x(parameter) is always between zero and one (inclusive)

Explanation / Answer

Both of the statements are false.

Explanation -

If the bootstrapping procedure and the formation of the confidence interval were performed correctly, it means the same as any other confidence interval. From a frequentist perspective, a 95% CI implies that if the entire study were repeated identically infinte number of times, 95% of such confidence intervals formed in this manner will include the true value.

Similarly a 99% bootstrap confidence interval for a parameter means that if you repeat the entire syudy many times, then 99% of the confidence intervals formed in this manner will include the true value.

This true value is the actual value of the parameter which will not necessarily be between 0 and 1. It can take any finite value.

not, but you won't know which.

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