Hypothesis or Significance Testing

1) Make a drawing of the sampling distribution for the null hypothesis and shade in the area representing the p-value. Remember, the mean on the drawing always matches with the m  given in Ho (see below).

2) Always use a parameter, never a statistic when stating the a hypothesis. State the null and alternative hypothesis mathematically one of three ways (note that Ho always has the same form):

Examples:   Ho: m = 12      Ha: m < 12     (Shade the tail on the left side of the sampling distribution drawing.)
  Ho: m = 12      Ha: m > 12      (Shade the tail on the right side of the sampling distribution drawing.)
  Ho: m = 12      Ha: m ≠ 1 (Shade the tails on both sides of the sampling distribution drawing.)

3) Using a statistic, find the area under the curve which corresponds to the p-value.

4) State the definition of p-value using the number you have just calculated.

Example for p-value = 3%:  The probability of obtaining a test statistic as extreme or more extreme than the one obtained is 3%, assuming Ho is true.

If Alpha is Given

5) Decide whether to reject or fail to reject the null hypothesis based on comparing the p-value with alpha.

  • If: p-value ≤ alpha level   reject Ho
  • If: p-value > alpha level   fail to reject Ho

6) Write an English language sentence summarizing your findings. For example if the null is rejected you might write:

Example 1) Ho rejected: The sample is statistically significant at the alpha level  (p=?) therefore we reject the null hypothesis and accept the alternative hypothesis that Bubba's magic pills caused a weight loss in the subjects who took them.

Example 2) Ho accepted: The sample is not statistically significant at the alpha level  (p=?), therefore, we fail to reject the null hypothesis. There is not sufficient evidence to accept the alternative hypothesis that Bubba's magic pills caused a weight loss in the subjects who took them.

If Alpha is Not Given

5) Skip this step

 

6) Write an English language sentence summarizing your findings stating whether there is or is not strong statistical evidence for rejecting the null hypothesis. This is based on your judgment

Example 1) Ho rejected: The sample provides strong statistical evidence (p=?) for rejecting the null hypothesis and accepting the alternative hypothesis that Bubba's magic pills caused a weight loss in the subjects who took them.

Example 2) Ho accepted: The sample does not provide strong enough statistical evidence (p=?) for rejecting the null hypothesis, hence, we cannot accept the alternative hypothesis that Bubba's magic pills caused a weight loss in the subjects who took them.