1. Chapter 9 Day 2

2. Warm-up  If students picked numbers completely at random from the numbers 1 to 20, the proportion of times that the number 7 would be picked is 0.05. When 15 students picked a number “at random” from 1 to 20, 3 of them picked the number 7. Identify the parameter and accompanying statistic in this situation.

3. Homework Solutions

4. Example

6. The Bias of a Statistic  The statistic used to estimate a parameter is unbiased if the mean of its sampling distribution is equal to the true value of the parameter being estimated.

8. The variability of the statistic  The variability of a statistic is described by the spread of its sampling distribution. This spread is determined by the sampling design and size of the sample. Larger samples give smaller spread.

9. The variability of the statistic  As long as the population is much larger than the sample (say, at least 10 times as large), the spread of the sampling distribution is approximately the same for any population size.  So in other words... A scoop of 50 M&Ms would have the same distribution regardless of if it was a sample for a truckload of M&Ms or a bucket of M&Ms

10. Bias vs. Variability

11. RESULTS - Summary  If n is “large” enough (n is approaching N, n is getting bigger)  Then three things occur…  1. The shape of the distribution become approximately normal (bell shaped)  2. The mean of the sampling distribution equals the mean of the population.  3. The standard deviation of the sampling distribution will become smaller (determined by your choice of n)