1. Errors & Power

2. 2 Results of Significant Test 1. P-value < alpha 2. P-value > alpha Reject H o & conclude H a in context Fail to reject H o & cannot conclude H a in context

3. Significance Level needs to be stated before the data is produced needs to be very small if Ho has been believed for years needs to be small if the consequences are drastic if we reject it and we shouldn’t have

4. What if we’re wrong Type I Error Type II Error These are not errors by people or the process; errors caused from variability and random chance

5. Type I Error Reject H o when it’s true P(Type I Error) = significance level “convicting and innocent person” draw Normal curve picture of this

6. Type II Error Failing 2 Reject H o when it’s false NOT accepting H o, or saying it’s true “let a guilty person go free”

7.                        

8. The manager of a fast foot restaurant wants to reduce the proportion of drive through customers who have to wait more than two minutes. Based on store records, the proportion of customers who had to wait more than two minutes was p = 0.63. To reduce this proportion, the manage assigns an additional employee to assist with drive through orders. During the next month, the manager will collect a random sample of drive through times and test the following hypotheses: H o : p = 0.63 H a : p < 0.63 where p = the true proportion of drive through customers who have to wait more than two minutes for their food. PROBLEM: Describe a Type I and Type II error in this setting and explain the consequence of each.

9. So why not just make our significance level very small so we don’t make a Type I Error?

10. Your company markets a computerized device for detecting high blood pressure. The device measures an individual’s blood pressure once per hour at randomly selected times throughout a 12-hr period. Based on sample results, the device determines whether there is significant evidence that the individual’s actual mean systolic pressure is greater than 130. If so, it recommends that person seek medical attention. a) State Ho, Ha, and identify your parameter. b) Describe Type I and Type II errors and their consequences c) Which significance level would you choose: alpha =.01,.05, or.10

11. Type II Error Fail 2 Reject the null when it is false So, we don’t know what the parameter is and we weren’t able to say it wasn’t what was stated in the null hypothesis.

12. POWER probability that the test will reject the H o at a given significance level when the specified alternative value is true (H a )

13.                        P(Type II Error) = 1 - Power

14. Power & Planning 1. Setting a Significance Level - what are the consequences of a Type I error? 2. Practical Importance - how different does the sample need to be from the hypothesized value to warrant a change? 3. Sample Size - all errors and power are connected to sample size as well as the fact that the larger the sample the more time and money will be used

15. Remember the fast food restaurant's hypotheses: H o : p = 0.63 H a : p < 0.63 where p = the true proportion of drive through customers who have to wait more than two minutes for their food. 1. Would the manager want to increase or decrease the significance level from 0.10? 2. For practical purposes, he decides that he needs to see the proportion drop to 0.53 to justify paying another employee. 3. Increase or decrease the sample size from 250? draw Normal curve picture of this

16. What Goes Up Must Come Down Lower significance level = Lower P(Type I Error)= Increase P(Type II Error) or Higher sample size = Increase Power = Decrease P(Type II Error)

17. You manufacture and sell a liquid product whose electrical conductivity is supposed to be 5. You plan to make 6 measurements of each lot of product. If the product meets specifications, the mean of many measurements will be 5. You will therefore test H0: mu = 5 Ha mu doesn’t = 5 If the true conductivity is 5.1, the liquid is not suitable for its intended use. You learn that the power of your test at the 5% significance level against the alternative mu = 5.1 is 0.23 a) Explain what power = 0.23 means b) Keeping alpha the same, could you increase your power by increasing or decreasing your sample size? c) If alpha = 0.10 instead of 0.05, would the power increase or decrease? d) Only change the alternative to 5.2, will your power increase or decrease?