Introduction to Hypothesis Testing II PowerPoint Presentation

P-Value Approach

• The p-value is the probability of obtaining a test statistic at least as extreme as the test statistic we calculated from the sample.
• The p-value is also known as the observed significance level.  
• It adds a degree of significance to the result of the hypothesis.
• We can now determine how strongly we “reject” or “fail to reject” the null hypothesis.
• If p-value < α, we reject the null hypothesis. If the p-value ≥ α, we fail to reject the null hypothesis.
• The farther the p-value is from α, the stronger the decision.

Example

• Company packages salted and unsalted peanuts in 16 – ounce sacks. The company’s filling strives for an average fill amount equal to 16 ounces.

    Suppose, z = 3.32 and α = 0.10
    then the p- value = 2(0.0005) = 0.0010.
    Decision Rule:
    Since the p-value = 0.0010 < α = 0.010, we reject H0
    and conclude that the average filling amount is not equal to 16 ounces