Problems

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One-Sample t-Test

Probability and Statistics

Medium

Given a sample x and a hypothesized population mean μ₀, compute the one-sample t-statistic.

One-Sample t-Statistic:

t = \frac{\bar{x} - \mu_{0}}{s / \sqrt{n}}

Where: x̄ = sample mean, s = sample standard deviation, n = sample size

Sample standard deviation (Bessel correction):

s = \sqrt{ \frac{1}{n - 1} \sum_{i=1}^{n} (x_i - \bar{x})^{2} }

Function Arguments

x: list or array - Sample observations
mu0: float - Null hypothesis mean (μ₀)

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Examples

Input: x=[2.1, 2.4, 1.9, 2.6, 2.0], mu0=2.0

Output: t_stat≈1.53

mean=2.20, std≈0.274, t=(2.20-2.0)/(0.274/√5)

Input: x=[3.0, 5.0], mu0=4.0

Output: t_stat=0.0

mean=4.0 equals mu0

Input: x=[1.0, 1.5, 2.0], mu0=3.0

Output: t_stat≈-5.20

negative t-statistic (sample mean < mu0)

Hint 1

Compute sample mean with np.mean().

Hint 2

Use np.sqrt() for sample standard deviation.

Hint 3

Standard error is s / np.sqrt().

Requirements

Return scalar float (t-statistic)
Must convert x to NumPy array
Use Bessel correction (n-1 denominator)
No external statistics libraries

Constraints

len(x) ≥ 2
NumPy only; time limit: 300ms

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