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What is a hypothesis test?

In statistics, as in everyday life, we tend to make hypotheses to predict what we don’t know. We might say, “I think it’s going to rain today,” or “the average height of the Italian population is the same as the average height calculated from samples.” However, a hypothesis cannot be accepted as true without proof; we can’t just believe everything we or someone else hypothesizes. A hypothesis can be rejected or not rejected. To determine whether our hypothesis should be rejected, we need to perform a hypothesis test.

To conduct a hypothesis test, the following ingredients are necessary:

1) A hypothesis framework; this includes a null hypothesis (H0), which is the hypothesis under examination and considered true unless proven otherwise, and an alternative hypothesis (H1), which is logically the opposite of H0.
2) An accepted error level. This is a numerical value indicating the degree of error we are willing to accept when rejecting H0. This is denoted by the symbol alpha. Using an alpha value of 0.05 means we accept a 5% chance of making an error when rejecting H0. Specifically, there are two types of errors in this context: Type I Error (rejecting H0 when it should be accepted) and Type II Error (not rejecting H0 when it should be rejected).

3) A test value; this is a numerical value calculated using specific formulas to determine whether H0 should be rejected. Remember, a statistical test, like the z-test, follows a decision rule that helps us determine if H0 should be rejected or not.
4) We also need a method to understand if the calculated statistical test value used to decide whether to reject H0 is reliable or by chance. Therefore, the p-value is needed, and ideally, this should be accompanied by a confidence level. Remember: the p-value tells us the probability of obtaining the test statistic by chance. The confidence interval is a numerical range of the variable of interest within which we assume the true value of the hypothesized variable falls a certain percentage of the time when the experiment is repeated multiple times. This percentage is called the confidence level, which is generally set to 95%.

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