Question

To create a confidence interval from a bootstrap distribution using percentiles, we keep the middle values and chop off a certain percent from each tail.
(a) What percent of values must be chopped off from each tail for a 95% confidence interval?
(b) If the bootstrap distribution contains values for 1000 bootstrap samples, how many should be chopped off at each end to produce a 95% confidence interval?

Answer 1

Answer:

a

 $\frac{\alpha }{2} = 2.5 \%$

b

  $N = 25$

Step-by-step explanation:

From the question we are told that

   The number of bootstrap samples is  n =  1000

From the question we are told the confidence level is  95% , hence the level of significance is    

      $\alpha = (100 - 95 ) \%$

=>   $\alpha = 0.05$

Generally the percentage of values that must be chopped off from each tail  for a 95% confidence interval is mathematically evaluated as

      $\frac{\alpha }{2} = \frac{0.05}{2} = 0.025 = 2.5 \%$

=>    $\frac{\alpha }{2} = 2.5 \%$

Generally the number of the bootstrap sample that must be chopped off to produce a 95% confidence interval is

      $N = 1000 * \frac{\alpha }{2}$

=>   $N = 1000 * 0.025$

=>   $N = 25$