Implement Welch T-Test from Scratch | Dataford Interview Questions

Write a function to perform a specific statistical test from scratch without using high-level libraries.

Implement a two-sided Welch independent-samples t-test for two numeric samples. Do not use SciPy, NumPy, pandas, or other statistical libraries. Return whether the null hypothesis of equal population means should be rejected at the supplied significance level.

Function: welch_t_test(sample_a, sample_b, alpha)

Inputs are nonempty numeric lists and a significance level alpha. Return True when the two-sided p-value is at most alpha, otherwise return False. Compute the t-statistic, Welch-Satterthwaite degrees of freedom, and p-value from scratch. Assume both samples have at least two observations and nonzero sample variance.

Constraints

2 <= len(sample_a), len(sample_b) <= 1000
Each sample contains finite real numbers
Both samples have nonzero sample variance
0 < alpha < 1
Do not use statistical libraries or numerical array libraries

Function Signature

def welch_t_test(sample_a, sample_b, alpha):

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