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## What is hypothesis?

Explain the errors in hypothesisBy:Jessika-K

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## Answers

We can assess the probability of two different types of error for a given significance level. These errors are typically termed Type I and Type II errors. Type I error involves cases where a hypothesis is true, but it is rejected because the test statistic exceeds the critical value for the significance level *α*. This might be considered a "false negative" result. (The above-mentioned case of a fair coin that so happens by chance to turn up heads an abnormally large number of times, resulting in the rejection of the hypothesis that the coin is fair, is an example of Type I error.) The probability of a Type I error occurring is the same as the significance level--in other words, the probability of a Type I error decreases with decreasing *α*. Recall that for a random variable (or test statistic) *X*,

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Type II error occurs when the null hypothesis is false, but the data does not indicate that it should be rejected. This situation could be considered a "false positive" result. Such a case might involve a loaded coin that happens to have a fair distribution of heads and tails in a certain series of flips. The probability that a Type II error occurs is the same as the probability that the random variable (or test statistic) does *not* exceed the critical value *c* if the alternative hypothesis is assumed to be true:

_{}

The probability *β* is therefore the probability that a Type II error will not occur.

In light of these errors, we can see that the choice of *α* (and therefore *β*) is not purely arbitrary--this choice has a significant effect on whether the probability that the analysis yields a correct result. Although we will not go into further depth on appropriate selection of *α* (or, perhaps more appropriately, *c*) such that the probability of errors is minimized, it is important that you remain aware that your choice of *α* is not without consequence.

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