7.4 part 2
- 1. 7.4 ESTIMATING 1 – 2 AND P1 – P2
- 2. Confidence Intervals for the difference between two population parameters In this section, we will use samples from two populations to create confidence intervals for the difference between population parameters. All the examples of this section will involve independent random samples.
- 3. Confidence Intervals for the difference between two population parameters There are several types of confidence intervals for the difference between two population parameters Confidence Intervals for 1 – 2 (1 and 2 known) Confidence Intervals for 1 – 2 (1 and 2 Are Unknown) Confidence Intervals for 1 – 2 (1 = 2) Confidence Intervals for p1 – p2
- 4. How to Interpret Confidence Intervals for Differences
- 5. Confidence Intervals for 1 – 2 (1 and 2 known)
- 6. Confidence Intervals for 1 – 2 (1 and 2 known)
- 7. Confidence Intervals for 1 – 2 (1 and 2 Are Unknown)
- 8. Confidence Intervals for 1 – 2 (1 and 2 Are Unknown)
- 9. Estimating the Difference of Proportions p1 – p2 the difference of two proportions from binomial probability distributions
- 10. Estimating the Difference of Proportions p1 – p2 Requirements Consider two independent binomial experiments
- 11. Estimating the Difference of Proportions p1 – p2
- 12. Example Page 381 In his book Secrets of Sleep, Professor Borbely describes research on dreams in the Sleep Laboratory at the University of Zurich Medical School. During normal sleep, there is a phase known as REM (rapid eye movement). For most people, REM sleep occurs about every 90 minutes or so, and it is thought that dreams occur just before or during the REM phase. Using electronic equipment in the Sleep Laboratory, it is possible to detect the REM phase in a sleeping person. If a person is wakened immediately after the REM phase, he or she usually can describe a dream that has just taken place. Based on a study of over 650 people in the Zurich Sleep Laboratory, it was found that about one- third of all dream reports contain feelings of fear, anxiety, or aggression. There is a conjecture that if a person is in a good mood when going to sleep, the proportion of “bad” dreams (fear, anxiety, aggression) might be reduced. Suppose that two groups of subjects were randomly chosen for a sleep study. In group I, before going to sleep, the subjects spent 1 hour watching a comedy movie. In this group, there were a total of n1 = 175 dreams recorded, of which r1 = 49 were dreams with feelings of anxiety, fear, or aggression. In group II, the subjects did not watch a movie but simply went to sleep. In this group, there were a total of n2 = 180 dreams recorded, of which r2 = 63 were dreams with feelings of anxiety, fear, or aggression.
- 13. Example Page 381 a) Check Requirements Why could groups I and II be considered independent binomial distributions? Why do we have a “large- sample” situation? Solution: Since the two groups were chosen randomly, it is reasonable to assume that neither group’s responses would be related to the other’s. In both groups, each recorded dream could be thought of as a trial, with success being a dream with feelings of fear, anxiety, or aggression.
- 15. Example Page 381 Interpretation What is the meaning of the confidence interval constructed in part (b)? Solution: We are 95% sure that the interval between – 16.6% and 2.6% is one that contains the percentage difference of “bad” dreams for group I and group II.
- 16. Assignment Page 385 #9, 10, 17, 21, 22