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### Student T-test Power Analysis

Unsolved
###### Prob. and Stats

Difficulty: 2 | Problem written by Junaid Ahmed
##### Problem reported in interviews at

A student T-test power analysis will produce a p-value that indicates if the samples are identical or if there's a statistical difference between them. It works on the basis of four parameters: effect, power, alpha, and ratio.

Alpha is the probability of eliminating the null hypothesis when it becomes true.

If the value of alpha is 0.05 then there's a 5% chance of difference exists when there is no actual difference.

The effect defines the difference between the means in terms of the number of standard deviations.

The statistical power defines that our test has an 80% chance of ending with a p-value less than 5% if the power is 80%.

The ratio is the percentage of a number of samples to the other samples. If both samples have the same number of observations then the ratio is 1.0. If the second sample is less than the first then it is 0.5

How we can implement it in Python?

Python provides a library named stats model to implement this.

Import TTestIndPower function from the statsmodels.stats.power

Create a TTestIndPower instance.

Implement the solver_power function with four parameters and an additional argument named nobs1 that will be declared as None. It will tell the function what to calculate.

This whole function will return the sample size for the experiment.

##### Sample Input:
<class 'list'>
e: 0.8
a: 0.05
p: 0.8

##### Expected Output:
<class 'float'>
25.524572500479444

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