What Is True Positive

  Statistical hypothesis test is one of the true positive tests. A statistical test method is similar to a trial. Here are two hypotheses H0 and H1.The initial one is call null hypothesis, along with for the time being accepted. The next one is called alternative hypothesis. During a statistical hypothesis test, there are two types of wrong conclusions that can be drawn. They are type I error and type II error.

What is meant for Type I error - True positive:

 

          A Type I error occur while the researcher rejects a null hypothesis while it be true. The probability of commit a Type I error is call the significance level. This probability be as well called alpha, along with is frequently denoted through α.

What is meant for Type II error.

          A Type II error occurs while the researcher fail to reject a null hypothesis to is false. The probability of commit a Type II error is call Beta, along with is often denoted through β. The probability of not committing a Type II error is calling the Power of the test.

 

Example Problems regarding What is true positive:

 

Example 1 for what is true positive:

         In a sample of size 17 drawn from a normal population standard deviation is 3 can you say that population standard deviation is  4.

Procedure: Null hypothesis:

                  H0:The population standard deviation is 4

Test statistic:

`chi^2=(ns^2)/(sigma^2)` ,     `chi^2(n-1)`

 

Level of significance:

       α=0.05 at g% level of `chi^2`table value for 16 degrees of freedom is 26.3

Calculation:

        n=17,s=3,sigma=4

`chi^2=(17xx9)/(16)`  

      =153/16

      =9.5625

   Calculated value = 9.5625

   Table value = 26.3

   Calculated value < Table value

   Null hypothesis is accepted.

    The population of standard deviation is 4

Result: The population standard deviation is 4

Example 2:(what is true positive)

      In a sample of size 17 drawn from a normal population standard deviation is 6 can you say that population standard deviation is  4.

Procedure: Null hypothesis

                 H0:The population standard deviation is 4

Test statistic:

`chi^2=(ns^2)/(sigma^2)`           `chi^2(n-1)`

Level of significance:

      α = 0.05 at g% level of `chi^2`table value for 16 degrees of freedom is 26.3

Calculation:

       n = 17,s = 3,sigma = 4

`chi^2=(17xx36)/(16)`  

         = `612/16`

         = 38.25

   Calculated value = 38.25

   Table value = 26.3

   Calculated value > Table value

   Null hypothesis is not accepted.

Result: The population standard deviation is not 4.