1. Stat 321 – Day 22 Confidence intervals cont.

2. Reminders Exam 2  Average .79 Communication, binomial within binomial  Course avg >.80  Final exam 20-25% HW 7 due Tuesday Quiz 6 Thursday on HW 6 Lab 7 due Friday

3. Last Time – t-intervals When don’t know the population standard deviation (pretty much always!), can use the sample standard deviation but then, to compensate for the extra uncertainty, use a critical value from the t distribution instead of the normal distribution  t critical value depends on sample size (df =n-1)  Widens interval to achieve stated confidence level  Approaches z critical value as n increases Technical conditions:  Random sample  Normal population but robust

4. Example Given: n = 5; Sample mean = 41.8, sample SD = 2.39; 90% confidence df = 5-1= 4, t = 2.132 41.8 + 2.132(2.39/sqrt(5)) 41.8 + 2.28 (“margin of error”) (39.52, 44.08) I’m 95% confident that the population mean chest measurement is in this interval (39.8) How many militiamen are in this interval?

5. Prediction Intervals To specify range of plausible values of individuals, consider the prediction for the average and then that a typical deviation from the average is  … 41.8 + 2.132(2.39)sqrt(1+1/5) 41.8 + 5.58 We are 90% confident that a random Scottish militiaman’s chest is between 36.22in and 47.38in

6. Example 2 A Gallup poll conducted Dec 5-8, 2005 by phoning a randomly selected sample of 1,013 adults, found that 66% of Internet users never read blogs “The margin of error is at most 3 percentage points.”

7. Example 2 Let p represent the proportion of all adult internet users who never use blogs  Sample proportion vs. population proportion? Apply this method to a population proportion  What use for estimate?  What use for standard deviation?  What use for critical value?

8. Sample proportion? = X/n where X is binomial (n, p) Expected value? Standard deviation? Shape? Confidence interval?

9. Confidence Interval for p (not  ) Technical conditions: Data are SRS from population of interest

10. Some Precautions Finding voters  Margin-of-error doesn’t measure “non-sampling” errors Alien visits U.S. Senate, wants to estimate proportion of humans who are female  Biased sample  Confidence interval not needed if one’s data is from population, not sample We are 100% confident that p =.16! Claimed to vote…

11. For Tuesday Back to Ch. 6! HW 7  Note addition to exercise 33 in problem 4