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Hypothesis testing is the standard procedure in statistics for testing a hypothesis, or claim, about population parameters.
IN CONTEXT
Suppose a Liter O'Cola company has a new Diet Liter O'Cola, which they claim is indistinguishable from Classic Liter O'Cola. They obtain 120 individuals to do a taste test.
If their claim is true, some people will be able to identify the diet soda just by guessing correctly. What percent of people will do that? You'd think it would probably be around 60 people, which is 50% --50% would guess correctly and 50% would guess incorrectly, simply based on guessing, even if the Diet Cola was indistinguishable from the Classic Cola.
Now, suppose that you didn't get an exact 50/50 split. Suppose 61 people correctly identified the diet Cola. Would that be evidence against the company's claim? Well, it's more than half, but it's not that much more than half. We would say no. Sixty-one isn't that different from 60. Therefore, it's not really evidenced that more than half of people can correctly identify the diet soda
Suppose that 102 people of the group were able to identify the diet cola correctly. Is that evidence against the company's claim? In this case, 102 is significantly more than half. We would say that this would be evidence that at least some of the people could taste the difference. Even if some of those 102 were guessing, it's evidence that at least some of those 102 can taste the difference.
Now, the question posed to us with the 102 is if the people were guessing randomly just by chance, what would be the probability that we would get 102 correct answers or more? Isn't it possible that 102 out of 120 could correctly pick the diet cola just by chance? Anything is possible.
However, if this was a low probability, then the evidence doesn't really support the hypothesis of guessing. In fact, it would appear that some people can taste the difference.
With hypothesis testing, there are two hypotheses that are pitted against each other.
EXAMPLE
Refer back to the competing hypotheses from above. The null hypothesis will be that "Liter O'Cola claims that 50% of people will correctly select the diet cola. We will state the null hypothesis as the true proportion of people who can correctly identify the diet soda, p, is equal to 1/2.In this example, if significantly more than half of the cola drinkers in our sample of 120 can correctly select the diet soda, we would reject the null hypothesis where Liter O'Cola claims that 50% of people will correctly select diet cola by chance.
If we reject the null hypothesis, then we are saying that we are in favor of the alternative hypothesis, which states that there is convincing evidence that more than half of people will correctly identify the diet cola.
Now, significantly more than half is a loose term. How many is that? It was decided that 102 was probably significant, while 61 probably wasn't that significant. We'll leave that definition for another time. On the other hand, if not significantly more than half of the participants select the diet soda, then you would fail to reject the null hypothesis. For instance, the 61 is not significantly more than half of the participants, and so you'd fail to reject the null hypothesis.
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