10/21/2009

Discussion of simulation activity / Interpreting confidence intervals

• The behavior of C.I.'s
  • Simulate the drawing of 50 simple random samples of size 100 from a population with p = 0.6.
  • Use Minitab to calculate the 90% C.I. for the population proportion for each of your 50 samples.
  • Verify the caclulations by checking the interval given for the first sample.
  • How many of your 50 C.I.'s contain the true mean?
• How does this simulation exercise help you interpret confidence intervals?

A modified approach for small samples

• An exact confidence interval
• A slight modification to the large sample procedure

Choosing the sample size

• Example - You wish to use a random sample of size n to construct an approximate C.I. for p (pi) that will have margin of error no greater than 0.05. How large should n be if you want your approximate confidence in the interval to be 95%?

Confidence intervals for a population mean

• When the population standard deviation is known (VERY UNREALISTIC)
• When the population standard deviation is unknown (WIDELY USED)
• Example - Exercise 9.44 on p. 401

Relationship between normal and t-distributions

• There is a different t distribution for each sample size.
• The degrees of freedom for this statistic comes from the standard deviation s.
• t distributions are very similar to the N(0,1) distribution. The major difference is that t distributions have more area in the tails than the N(0, 1) distribution.
• As the sample size increases, t distributions get closer to the N(0, 1) distribution.

Class Exercises

• 9.31, 9.41, 9.43, 9.47

Please complete your reading of Chapter 9 and read Section 10.1 for class on Friday.