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7.4 part 2 7.4 part 2 Presentation Transcript

  • 7.4 ESTIMATING 1 – 2 AND P1– P2
  • Confidence Intervals for thedifference between two populationparameters 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.
  • Confidence Intervals for thedifference between two populationparameters 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
  • How to Interpret Confidence Intervals for Differences
  • Confidence Intervals for 1 – 2 (1 and 2 known)
  • 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 and 2 Are Unknown)
  • Estimating the Difference of Proportions p1 – p2 the difference of two proportions from binomial probability distributions
  • Estimating the Difference of Proportions p1 – p2 Requirements Consider two independent binomialexperiments
  • Estimating the Difference of Proportions p1 – p2
  • Example Page 381In his book Secrets of Sleep, Professor Borbely describes research on dreamsin the Sleep Laboratory at the University of Zurich Medical School. Duringnormal sleep, there is a phase known as REM (rapid eye movement). For mostpeople, REM sleep occurs about every 90 minutes or so, and it is thought thatdreams occur just before or during the REM phase. Using electronic equipmentin the Sleep Laboratory, it is possible to detect the REM phase in a sleepingperson. If a person is wakened immediately after the REM phase, he or sheusually can describe a dream that has just taken place. Based on a study ofover 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. Thereis a conjecture that if a person is in a good mood when going to sleep, theproportion 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 comedymovie. In this group, there were a total of n1 = 175 dreams recorded, ofwhich 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. Inthis group, there were a total of n2 = 180 dreams recorded, of which r2 = 63were dreams with feelings of anxiety, fear, or aggression.
  • Example Page 381a) 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 toassume that neither group’s responses would be related to theother’s.In both groups, each recorded dream could be thought of as atrial, with success being a dream with feelings of fear, anxiety, oraggression.
  • Example Page 381
  • 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 thepercentage difference of “bad” dreams for groupI and group II.
  • Assignment Page 385 #9, 10, 17, 21, 22