1. Stage 1 Statistics students from Auckland university Sampling variability & the effect of sample size

2. Recap from last week… 1. What is PPDAC short for? 2. What are three types of investigative questions? 3. What does a good investigative question need to have? 4. Give two reasons we might take a sample rather than look at the whole population

3. Recap from last week… 5. Give four words that could be used to describe the shape of a distribution 6. You and your neighbour both take a random sample from the same population. Your neighbour sees that your work is different from theirs and says that you must have done something wrong. What would you say to your neighbour? 7. What is “sampling error”?

4. Stage 1 Statistics Data  Internet based survey  Stage 1 students at Auckland University in 2009  Students invited to complete the survey and gain 2 marks towards their first assignment, marked out of ten.

5. Problem  I wonder what the median weight of Stage 1 Statistics students at Auckland University is?

6. Plan  Simple random sample of 30 students please.

7. Data  SRS of 30 students

8. Analysis  Plot dot plot on axes  Add box plot above  Note the 5 point summary  {Minimum, lower quartile, median, upper quartile, maximum}

9. Analysis  We’ll come back in a minute here and compare our n = 15 with our n = 30 distributions

10. Conclusion Estimate Parameter Population Median Data Sample  From my sample data, my best estimate of the population parameter is that the median weight for all Stage 1 statistics students is … This is a Point estimate

11. Increasing sample size… NOTE:  Increasing the sample size increases the cost of the survey.  As long as the sampling method is sound there is very little benefit in increasing the sample size above 35.  We would get little extra useful information.