Bootstrap-t Confidence Interval

Problem

Return the bootstrap-t confidence interval for the mean using n_boot resamples drawn with a self-contained Lehmer RNG seeded with seed (state = seed % 2147483647, next = state * 48271 % 2147483647). Convert z_crit to a tail probability with the normal CDF, take the alpha/2 and 1-alpha/2 percentiles of the studentized resample statistics with linear interpolation, and pivot them back to the mean scale. Return [0.0, 0.0] when n < 2 or n_boot <= 0.

Hint

Studentize each resample before taking percentiles.

Test cases

case 1

in: [[1,2,3,4,5],200,7,1.96]

expected: [0.7639320225002102,4.582887063211015]

case 2

in: [[10,20,30,40],300,99,1.645]

expected: [14.88700206305137,44.364916731037084]

case 3

in: [[5],10,1,1.96]

expected: [0,0]

case 4

in: [[],10,1,1.96]

expected: [0,0]

case 5

in: [[1,2],50,3,1.96]

expected: [1.5,1.5]

Starter codePython

import math
def bootstrap_t_ci(data, n_boot, seed, z_crit):
    # Your code here
    pass

5 test cases · run your code against them in the editor