Hypothesis Testing

# Hypothesis Testing - Hypothesis Testing Hypothesis Testing...

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Hypothesis Testing Hypothesis Testing Whenever we have a decision to make about a population characteristic, we make a hypothesis. Some examples are: €€€€€€€ μ > 3 or μ 5. Suppose that we want to test the hypothesis that μ 5 . Then we can think of our opponent suggesting that μ = 5 . We call the opponent's hypothesis the null hypothesis and write: H 0 : μ = 5 and our hypothesis the alternative hypothesis and write H 1 : μ 5 For the null hypothesis we always use equality , since we are comparing μ with a previously determined mean. For the alternative hypothesis, we have the choices: < , > , or . Procedures in Hypothesis Testing When we test a hypothesis we proceed as follows: 1. Formulate the null and alternative hypothesis. 2. Choose a level of significance. 3. Determine the sample size. (Same as confidence intervals) 4. Collect data.

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5. Calculate z (or t ) score. 6. Utilize the table to determine if the z score falls within the acceptance region. 7. Decide to a. Reject the null hypothesis and therefore accept the alternative hypothesis or b. Fail to reject the null hypothesis and therefore state that there is not enough evidence to suggest the truth of the alternative hypothesis. Errors in Hypothesis Tests We define a type I error as the event of rejecting the null hypothesis when the null hypothesis was true . The probability of a type I error ( α ) is called the significance level. We define a type II error (with probability β ) as the event of failing to reject the null hypothesis when the null hypothesis was false . Example Suppose that you are a lawyer that is trying to establish that a company has been unfair to minorities with regard to salary increases. Suppose the mean salary increase per year is 8% . You set the null hypothesis to be H 0 : μ = .08 H 1 : μ < .08 Q. What is a type I error? A. We put sanctions on the company, when they were not being discriminatory. Q. What is a type II error? A. We allow the company to go about its discriminatory ways. Note: Larger α results in a smaller β , and smaller α results in a larger β . Hypothesis Testing For a Population Mean The Idea of Hypothesis Testing
Suppose we want to show that only children have an average higher cholesterol level than the national average. It is known that the mean cholesterol level for all Americans is 190 . Construct the relevant hypothesis test: H 0 : μ = 190 H 1 : μ > 190 We test 100 only children and find that x = 198 and suppose we know the population standard deviation σ = 15. Do we have evidence to suggest that only children have an average higher cholesterol level than the national average? We have z is called the test statistic . Since z is so high, the probability that Ho is true is so small that we decide to reject H 0 and accept H 1 . Therefore, we can conclude that only children have a higher cholesterol level on the average then the national average.

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