Hypothesis Testing

Hypothesis Testing involves the following:

  1. Null / Alternative . . . . . Hypotheses
  2. Testing Procedures
  3. Type I, Type II . . . . errors
  4. One / Two . . . . sided Hypothesis Tests
  5. Upper / Lower . . . . Critical Values
  6. z values
  7. p values

 

 

At what point can you accept the sample mean as the true population mean?

 

You reject it when it IS CORRECT   = Type I error

You accept it when it is NOT CORRECT = Type II error

 

The statement believed to be true H0 = the sample mean is thought to approximate the population mean

 

So, the null hypothesis is rejected. THe next scenario is Ha= the sample mean is thought to approximate the population mean.

 

A two sided test is when Ha, is set to (not equal) the test indicator. Ha is (not equal) to the test indicator.

What z values are associated with the area under the curve (bzw the shaded areas)? For a two sided test - 1,96 and + 1,96.

 

Determining then the critical values for the two sided test, the sample mean is not equal to the population mean:

 

+/- 1,96 = upper/critical value - sample mean / (standard deviation * square root of the sample population size)

 

(critical values should differ by the same amount as the sample size). Since the test is for H0 ..if the mean is between the upper and lower critical values, then the null hypothesis is accepted. If the mean falls outside of the critical value, then the alternative hypothesis is accepted.

 

What if the test was such that the null hypothesis states the mean is equal to or greater than a given population mean? Left side of the curve = (negative), Right side of the curve = (positive).  z = - / + 1,645 when alpha is 0,05. *But, you only calculate the upper limit for one side. + / - 1,645 is associated with 90%.

 

Choose a smaller alpha if you want to avoid making a Type I error.