# Hypothesis

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Errors in Hypothesis Testing
Hypothesis testing is wide spread not only in the statistics but also in natural and social
sciences. When carrying out hypothesis testing, some errors occur and they are unavoidable.
They include:
Type I errors
These errors occur when we reject a true null hypothesis.
According to McNabb, Type I errors are caused by the alpha ) level during the
hypothesis testing with higher levels of α causing an increased rate of type I errors. The notion
that α is the probability of Type I is not true, but it is, however, true if the hypothesis is correct.
In the cases of false hypothesis then it is impossible to make type I errors.
Example
Hypothesis: "Adding water to toothpaste prevents the teeth from developing cavities."
Null hypothesis (H0): "Water added to toothpaste does not affect cavities."
Testing the null hypothesis experimental data with an intention to nullify it with evidence
to the contrast.
A type I error occurs when detecting the effect of adding water to toothpaste protects
tooth against developing cavities and is not present. Therefore the null hypothesis is true, but this
null hypothesis is rejected based on inadequate experimental data.

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Type II errors
They happen when we don’t reject a false null hypothesis.
Type II errors are typically not errors, and it occurs when the statistical test does not
provide sufficient proof that the null hypothesis is wrong. It is mainly a mistake that happens
during a statistical test if the researcher should not be quick to conclude that the null hypothesis
is true if there is no sufficient evidence. However, the researcher should consider the test
inconclusive. It occurs only when the hypothesis is false. The probability of a type two errors is
called beta when the assumption is false. Power is a term used to refer to the likelihood of
rejecting the hypothesis correctly, and it should be equal to (1-beta). (McNabb, David E. Pg.
160).
Example
In a t-test, the sample µ, with null hypothesis "µ = 0" and alternate hypothesis "µ > 0",
the Type II error occurs relative to the general alternative hypothesis "µ > 0",

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SURNAME1 Student’s name Professor’s Name Course Date Errors in Hypothesis Testing Hypothesis testing is wide spread not only in the statistics but also in natural and social sciences. When carrying out hypothesis testing, some errors occur and they are unavoidable. They include: Type I errors These errors occur when we reject a true null hypothesis. According to McNabb, Type I errors are caused by the alpha (α) level during the hypothesis testing with higher levels of α causing an increased rate of type I errors. The notion that α is the probability of Type I is not true, but it is, however, true if the hypothesis is correct. In the cases of false hypothesis then it is impossible to make type I errors. Example Hypothesis: "Adding water to toothpaste prevents the teeth from developing cavities." Null hypothesis (H0): "Water added to toothpaste does not affect cavities." Testing th ...
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