# How to do a two-sided hypothesis test for a sample mean (in Python, using SciPy)

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Say we have a population whose mean $\mu$ is known. We take a sample $x_1,\ldots,x_n$ and compute its mean, $\bar x$. We then ask whether this sample is significantly different from the population at large, that is, is $\mu=\bar x$?

## Solution

This is a two-sided test with the null hypothesis $H_0:\mu=\bar x$. We choose a value $0\leq\alpha\leq1$ as the probability of a Type I error (false positive, finding we should reject $H_0$ when itâ€™s actually true).

 1 2 3 4 5 6 7 8 9 10 11 12 from scipy import stats # Replace these first three lines with the values from your situation. alpha = 0.05 pop_mean = 10 sample = [ 9, 12, 14, 8, 13 ] # Run a one-sample t-test and print out alpha, the p value, # and whether the comparison says to reject the null hypothesis. t_statistic, p_value = stats.ttest_1samp( sample, pop_mean ) reject_H0 = p_value < alpha alpha, p_value, reject_H0
 1 (0.05, 0.35845634462296455, False)

In this case, the sample does not give us enough information to reject the null hypothesis. We would continue to assume that the sample is like the population, $\mu=\bar x$.