We do not reject the null hypothesis and we can then conclude that the status quo (null) is true. 2. We reject the null hypothesis and we cannot conclude that the status quo (null) is true. Hypothesis testing relies on “proof by contradiction”. The author uses the analogy of our legal system to explain this concept. Ultimately we never prove with certainty the null hypothesis to be true. Because of this limitation we can never accept the null hypothesis. Instead the most we can say is that we do not have enough evidence to reject the null hypothesis. H 0 : The defendant is innocent (status quo); H 1 : The defendant is guilty The two conclusions are: 1. Reject the null hypothesis The defendant is guilty 2. Fail to reject the Null hypothesis The defendant is not guilty. There is always going to be a risk of drawing the wrong conclusion because we are using data from a sample to draw conclusions about the population. The two types of errors we could make are: (p.386) 1. Type I Error: occurs when the null hypothesis is rejected but is reality is true. The probability of making a type 1 error is known as, a, the level of significance. 2. Type II Error: occurs when we fail to reject the null hypothesis when in reality it is not true. The probability of making a type two error is known as β. The only way to reduce the risk of making both error is to increase the sample size. We will look at how to perform hypothesis tests for three scenarios: 9.2 Hypothesis Testing for the Population Mean when σ is Known (p.388 Step 1: Identify the null and alternative hypotheses. Step 2: Set a value for the significance level, a.
Step 3: Determine the appropriate critical value. One-Tailed Test: Find z-score at z a in the tail Two-Tailed Test: Find z-score with _______ in the tail We can use the excel function =norm.s.inv to get the critical z-score.
- Spring '13
- Null hypothesis, Statistical hypothesis testing