Question

if we wish to obtain a 98% confidence intercal of a parameter using the bootstrap method, which percentiles of the resamples distribution will form the lower and upper bounds of the interval?

Answer 1

Lower bound = 1%

Upper bound = 99%

Explanation:

Given

I = Confidence Interval = 98%

First, we need to get alpha (α)

We get α by converting the confidence interval to decimal

α = 98%

α = 98/100

α = 0.98

The lower bound and the upper bound (using the bootstrap method) are calculated as follows;

Lower bound = (1 - α)/2

Upper bound = α + (1 - α)/2

Given that α = 0.98

Lower bound = (1 - α)/2 ---- substitute 0.98 for α

Lower bound = (1 - 0.98)/2 --- open bracket

Lower bound = 0.02/2 ---- divide

Lower bound = 0.01 --- convert to percentage

Lower bound = 1%

Given that α = 0.98

Upper bound = α + (1 - α)/2 --substitute 0.98 for α

Upper bound = 0.98 + (1 - 0.98)/2 --- open bracket

Upper bound = 0.98 + 0.02/2 ---- divide

Upper bound = 0.98 + 0.01

Upper bound = 0.99 --- convert to percentage

Upper bound = 99%

Hence, the lower bound is 0.01 and the upper bound is 99%