Hypothesis Tests

Let’s make it like the parameter we are interesting in testing is population mean

population mean = μ

population mean stated in the null hypothesis = μ0

We don’t know what is the true value of μ

So we study data and some information might let us think it could be greater than, less than, or it is not equal to the existing μ0 stated in the null hypothesis

So we propose in an alternative hypothesis, the population mean could be

H1: μ >μ0

H1: μ <μ0

H1: μ ≠ μ0

Let’s see the rejection region and acceptance region for population mean

null hypothesis stated that μ is this μvalue.

H0: μ =μ0

if the alternative value of μ  is greater than μ0, then the alternative hypothesis is

H1: μ >μ0

Then, if the data find the population mean to be a value greater than μ0 , you must reject the hull hypothesis population value of μ0

Therefore, population mean values that can cause the rejection of null hypothesis lie within a region of μ >μ0

In a line presentation, this rejection region of null hypothesis is drawn as shown below

Now, if data findings tell us the alternative hypothesis is less than the  stated in null hypothesis

H1: μ <μ0

Therefore, population mean values that can cause the rejection of null hypothesis lie within a region of μ <μ0

Now, if data findings tell us the alternative hypothesis is less than the  stated in null hypothesis

H1: μ ≠ μ0

Therefore, population mean values that can cause the rejection of null hypothesis lie within a region of μ ≠ μ0

Review Concepts before testing: Rejection region and Tails

DNA Pot (c) 2009 - Current