# Hypothesis Testing

Hypothesis testing was introduced by Ronald Fisher, Jerzy Neyman, Karl Pearson and Pearson's son, Egon Pearson.   Hypothesis testing is a statistical method that is used in making statistical decisions using experimental data.  Hypothesis Testing is basically an assumption that we make about the population parameter.

Key terms and concepts:

• Null hypothesis: Null hypothesis is a statistical hypothesis that assumes that the observation is due to a chance factor.  Null hypothesis is denoted by; H0: μ1 = μ2, which shows that there is no difference between the two population means.
• Alternative hypothesis: Contrary to the null hypothesis, the alternative hypothesis shows that observations are the result of a real effect.
• Level of significance: Refers to the degree of significance in which we accept or reject the null-hypothesis.  100% accuracy is not possible for accepting or rejecting a hypothesis, so we therefore select a level of significance that is usually 5%.
• Type I error: When we reject the null hypothesis, although that hypothesis was true.  Type I error is denoted by alpha.  In hypothesis testing, the normal curve that shows the critical region is called the alpha region.
• Type II errors: When we accept the null hypothesis but it is false.  Type II errors are denoted by beta.  In Hypothesis testing, the normal curve that shows the acceptance region is called the beta region.
• Power: Usually known as the probability of correctly accepting the null hypothesis.  1-beta is called power of the analysis.
• One-tailed test: When the given statistical hypothesis is one value like H0: μ1 = μ2, it is called the one-tailed test.
• Two-tailed test: When the given statistics hypothesis assumes a less than or greater than value, it is called the two-tailed test.

Statistical decision for hypothesis testing:

In statistical analysis, we have to make decisions about the hypothesis.  These decisions include deciding if we should accept the null hypothesis or if we should reject the null hypothesis.  Every test in hypothesis testing produces the significance value for that particular test.  In Hypothesis testing, if the significance value of the test is greater than the predetermined significance level, then we accept the null hypothesis.  If the significance value is less than the predetermined value, then we should reject the null hypothesis.  For example, if we want to see the degree of relationship between two stock prices and the significance value of the correlation coefficient is greater than the predetermined significance level, then we can accept the null hypothesis and conclude that there was no relationship between the two stock prices.  However, due to the chance factor, it shows a relationship between the variables.

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