1. Chapter 8: Estimation Section 5: Estimating and

2. ►T►T►T►Two samples are independent if the data values obtained from one are unrelated to the values from the other. ►T►T►T►The samples are dependent if each data value from one sample is paired in a natural way with a data value from the other sample.

3. Examples ► In a medical experiment, a sample of subjects is randomly divided into two groups. One group is given a specific treatment and the other group is given a placebo. After a certain period of time, both groups are measured for the same condition. ► A group of students in an English composition course is given a pretest. After the course, the same students are given a post-test.

4. Confidence Interval (large samples) Example (large sample) ► Suppose a biologist is studying data from Yellowstone streams. Results are summarized below: YEARSAMPLESIZEMEANSTANDARDDEVIATION1983-1988 n 1 = 167 x 1 = 5.2 s 1 = 1.9 1990-1993 n 2 = 125 x 2 = 6.8 s 2 = 2.3 -Are the samples dependent or independent? -Compute a 95% confidence interval for

5. Confidence Interval (small samples) (pooled variance) df =

6. Example (small sample) ► Suppose brain waves are being analyzed for a sleep study. Results are summarized below: GroupSAMPLESIZEMEANSTANDARDDEVIATION alcohol n 1 = 15 x 1 = 19.65 s 1 = 1.86 no alcohol n 2 = 14 x 2 = 6.59 s 2 = 1.91  Are the samples dependent or independent?  Compute a 90% confidence interval for

7. Confidence Interval for p1 – p2

8. Example ► Suppose two groups are randomly chosen for a sleep study. In group 1, the subjects watch a movie before going to sleep. 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 2, the subjects did not watch a movie. In this group, there were a total of n2 = 180 dreams recorded, of which r = 632 were dreams with feelings of anxiety, fear, or aggression. Compute a 95% confidence interval for p1 – p2.