Statistical Inference
Revisit statistical inference with a new dataset.
We'll cover the following
The key to the substantive question asked earlier is whether the male
and happy
variables are statistically independent of each other in the population. If they are independent of each other, then there’s no gender difference in selfreported happiness. If they aren’t independent of each other, then there is a gender difference in selfreported happiness. For a twoway contingency table of two discrete variables, statistical independence means that the joint probabilities are equal to the product of the marginal probabilities. In light of this information, the null and alternative hypotheses can be rephrased as follows:

Null hypothesis: The
male
andhappy
variables are statistically independent of each other. (Technically, the joint probability for each cell is equal to the product of the corresponding marginal probabilities, which holds for all four cells.) 
Alternative hypothesis: The
male
andhappy
variables aren’t statistically independent of each other. (Technically, the joint probability for at least one cell does not is equal to the product of the corresponding marginal probabilities.)
Chisquared test#
A commonly used test is the
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