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One-Sample t-Test

Probability and Statistics

Medium

Compute the one-sample t-statistic for observations $x_1,\ldots,x_n$ and hypothesized mean $\mu_0$ . First compute the sample standard deviation:

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

Then compute:

t = \frac{\bar{x}-\mu_0}{s/\sqrt{n}}

Here, $\bar{x}$ is the sample mean. If $s=0$ , return zero when $\bar{x}=\mu_0$ and signed infinity otherwise. Return the statistic as a Python float.

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Examples

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

Output: 1.53393

Explanation: The sample mean is above the hypothesized mean by about 1.53 standard errors.

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

Output: 0.0

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

Output: -5.196152

Hint 1

Compute centered = x - np.mean(x) before the corrected variance.

Hint 2

The standard error is sample_std / np.sqrt(x.size).

Requirements

Compute sample standard deviation with Bessel's correction
Divide the mean difference by the standard error
Handle zero sample variance as stated
Return a Python float

Constraints

x is a one-dimensional numeric list with at least two values
mu0 is finite
Use NumPy only

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