# Statistical Hypothesis Testing

**Topics:**Statistical hypothesis testing, Null hypothesis, Type I and type II errors

**Pages:**5 (982 words)

**Published:**June 19, 2013

Statistical Inference

Testing of Hypothesis

Type I Error:

Rejection of the null hypothesis when it is true is called a type I error.

Type II Error:

Acceptance of the null hypothesis when it is false is called a type II error. |Decision of the test for the Null Hypothesis |The Null Hypothesis is | | |True |False | |Accept |Correct decision |Incorrect decision | | | |Type II Error | |Reject |Incorrect decision |Correct decision | | |.Type I Error | |

Test Concerning Mean

One and Two tailed Tests:

A test procedure is called a one tailed test procedure if the alternative hypothesis is one sided. The test will be two tailed if the alternative hypothesis is two sided.

Example:

Let a specified value of population mean is 45. Construct the null and alternative hypothesis for the following questions; a) Do the sample data provide sufficient evidence to indicate that the population mean is greater than 45. [pic]leads to one tailed test (or right tailed test) b) Do the sample data provide sufficient evidence to indicate that the population mean is less than 45. [pic]leads to one tailed test (or left tailed test) c) Do the sample data provide sufficient evidence to indicate that the population mean is not equal to 45. [pic]leads to two tailed test (or both tailed test)

Level of Significance and Power of a Test:

• The probability of making type I error is called the level of significance of the test denoted by [pic] • The probability of making a type two error is denoted by [pic] and (1 - [pic]) is called the power of the test.

|Decision of the test for the Null |The Null Hypothesis is | |Hypothesis | | | |True |False | |Accept |Correct decision |Incorrect decision | | |P(Correct decision)=1-[pic] |Type two error | | | |P(type II error) = [pic] | |Reject |Incorrect decision |Correct decision | | |P(type I error)= [pic] |P(correct decision)=1-[pic] | | |= level of significance of the test |=Power of test. |

Rejection Rule and Conclusion:

Points to Note

i) Rejection of [pic] indicates that an extremely unlikely sample has been drawn which implies that [pic] is very likely to be false. ii) Failing to reject [pic] does not prove that [pic] is true. It implies that [pic] may be true. iii) In testing hypotheses, the assumption is always made that the sample used in the test process is a random sample. iv) It is assumed that the sampling distribution of the test statistic is known. v) [pic], [pic] and [pic] are determined before the test is carried out.

Formal Testing Procedure:

A hypothesis testing...

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