Distributions of a Sample Mean

Testing for Diabetes… A female patient is being tested for gestational diabetes. A glucose level of 140 mg/dL or more 1 hour after ingesting a sugar drink would suggest diabetes. A patient shows m = 136 mg/dL (with s = 5) after one such a test. Can the doctor safely conclude that the patient does not have diabetes? The doctor decides to order 3 more tests over the next 3 days and gets the same reading of m = 136 mg/dL . How does this affect the confidence she places in her diagnosis?

The Mean… A phone survey is conducted to determine how many hours of TV are watched in a household. This could be used to set the price for selling advertising, for example. Some of the most useful statistics that could be determined are: The mean number of hours of TV watched The standard deviation

Sample Means and Population Means We generally do not know the population mean (but assume it exists) We estimate the population mean by taking the mean of a SRS  sample mean

A Key Question… How accurate is our measure of the mean in the population? In other words – “How well does any one measure of sample mean represent the actual mean?”

Some fundamental ideas… If we measure the mean from “large” samples of a population then the “mean of the mean” should be very nearly equal to the true population mean See example 5.14

The Central Limit Theorem As n gets big (and as long as there is a finite standard deviation) then any sampling distribution of the sample mean becomes normal. This means that See example 5.19

Time for some applications… ooh .. This isn’t a math course?

Group work… 5.42 5.49 5.50 5.51 Indentify “n” Set up in N(m,s) form, use Z-score 5.49 Hint – see example 5.17 Draw this as a N(m,s) distribution 5.50 Similar to 5.49 5.51

In conclusion… Make sure to review the numerous formulae in this chapter Pick 4 or 5 questions from Chapter Exercises on pgs 409-413 and: Try to identify the specific statistical method appropriate Make sure to correctly identify “n” and “k” Try to solve!