If p-value & gt; α, we ‗ fail to reject H0‘, The data did not provide significant evidence to reject H0. Please note that we never ‗ accept H0‘. The problem of ‗ accepting‘ is that this wording makes it seem that we are convinced that the null hypothesis is true.( Business Statistics) Chapter 8 January 4, 2017 10 / 48 Introduction to Hypothesis Testing The p-value and Significance Level Hypothesis testing is meant to reject the null hypothesis when the evidence is convincingly against it. If we collect only a small sample, we may not see convincing evidence for the alternative hypothesis because the sampling error is so large. For instance, if we observed three births and observed two boys, we would not be willing to accept the hypothesis ‗ 2 / 3 of all births are boys‘ even though the data doesn‘ t provide evidence that it is false.( Business Statistics) Chapter 8 January 4, 2017 11 / 48 Hypothesis Testing for p Hypothesis Testing for p The pharmaceutical company is claiming a hypothesis, or wanting to show, that fewer than 20 % of the patients who use a particular medication experience side effects. In a clinical trial with 400 patients, they find 68 patients experienced side effects. Initially we would assume that 20 % or more of patients who use a particular medication experience side effects.( Business Statistics) Chapter 8 January 4, 2017 12 / 48 Hypothesis Testing for p Hypothesis Testing for p This can be written as: H0: 20 % or more of the patients who use a particular medication experience side effects. H1: Fewer than 20 % of the patients who use a particular medication experience side effects. We can also summarize this as: H0: p ≥ 0.20 H1: p & lt; 0.20 where p is the true proportion of patients who use a particular medication that experience side effects.( Business Statistics) Chapter 8 January 4, 2017 13 / 48 Hypothesis Testing for p Hypothesis Testing for p Once we have the hypotheses stated, we then need to calculate the