Hypothesis testing and t test using python
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hypothesis testing is a statistical method used to make decisions about a population based on sample data. it involves formulating a hypothesis, collecting data, and then determining whether to reject or fail to reject the hypothesis based on statistical evidence.
key concepts of hypothesis testing
1. **null hypothesis (h0)**: a statement that there is no effect or no difference. it is the hypothesis that researchers try to disprove.
2. **alternative hypothesis (h1)**: a statement that indicates the presence of an effect or a difference. it is what researchers aim to support.
3. **significance level (α)**: the threshold for rejecting the null hypothesis, commonly set at 0.05 or 0.01.
4. **p-value**: the probability of observing the test results under the null hypothesis. a low p-value indicates strong evidence against the null hypothesis.
5. **test statistics**: a standardized value that is calculated from sample data during a hypothesis test.
types of hypothesis tests
**z-test**: used when the population variance is known or the sample size is large (n 30).
**t-test**: used when the population variance is unknown and the sample size is small. there are three types:
one-sample t-test
independent two-sample t-test
paired sample t-test
in this tutorial, we will focus on the *t-test* using python.
one-sample t-test example
let's say we want to test if the average height of students in a class is different from 160 cm.
#### steps:
1. formulate the hypotheses:
null hypothesis (h0): the mean height is 160 cm.
alternative hypothesis (h1): the mean height is not 160 cm.
2. collect data (sample of heights).
3. perform the t-test.
4. interpret the results.
python implementation
we will use the `scipy` library to perform the t-test.
independent two-sample t-test example
now, let's say we want to compare the heights of two different classes of students.
#### steps:
1. formulate the hypotheses:
null ...
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