Hypothesis testing. Null vs alternative

This section serves as a main part of the course, building upon previous knowledge of confidence intervals, distributions, z-tables, and t-tables. It highlights that confidence intervals provide estimations, while hypothesis testing offers yes/no answers for decision-making. The video introduces the four steps in data-driven decision-making: formulating a hypothesis, finding the right test, executing the test, and making a decision.

A hypothesis is defined as "an idea that can be tested." The video distinguishes between an idea and a testable hypothesis, using the example of apple prices in New York. If "expensive" is defined with a specific price point, it becomes a testable hypothesis. Untestable ideas, like comparing future political administrations without data, are clarified as not statistical hypotheses.

The video introduces the key components of hypothesis testing: the null hypothesis (H0) and the alternative hypothesis (H1 or HA). Using the example of the mean data scientist salary from Glassdoor, the null hypothesis is stated as the status quo (e.g., salary is $113,000), and the alternative hypothesis covers all other possibilities (e.g., salary is not $113,000). The null hypothesis is assumed true until proven otherwise, similar to "innocent until proven guilty."

The video explains different types of hypothesis tests: two-sided (or two-tailed) and one-sided (or one-tailed) tests. The previous salary example is a two-sided test. A one-sided test is illustrated with a friend's claim about data scientists earning more than $125,000, where the null hypothesis would be that the salary is more than $125,000, and the alternative is that it is less than or equal to $125,000.

Important points regarding hypothesis testing are highlighted: test outcomes refer to the population parameter, not the sample statistic. Researchers generally aim to reject the null hypothesis, viewing it as the status quochallenged by the alternative hypothesis, which represents change or innovation. The video concludes by promising further examples and data-driven decision-making lessons.