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Draft curriculum 2006

Draft curriculum 2006. Statistical inference sampling variability estimate intervals sampling/ non sampling errors parameters estimates sample size effect margins of error variability of an estimate margin of error in the media.

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Draft curriculum 2006

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  1. Draft curriculum 2006 Statistical inference sampling variabilityestimateintervalssampling/nonsampling errors parametersestimatessamplesizeeffect marginsoferrorvariability of an estimate margin of error in the media A unit of work prepared and presented by:Marina Mcfarland & Anne Blundell (AGGS) Matt Regan (Stats Dept)

  2. Draft curriculum 2006: Statistical investigation (thinking) Level 6: - making informal inferences about populations from sample data and communicating findings Level 7: - using sample statistics to make point estimates of population parameters - recognising the effect of sample size on the variability of an estimate Level 8: - determining estimates and confidence intervals for mean, proportions and differences

  3. Draft curriculum 2006: Statistical investigation (thinking) Level 7 - identifying sampling and possible non-sampling errors in polls and surveys Level 8 - . . . interpreting margins of error

  4. What proportion of NZ Year 5-10 pupils (mainly) run around at lunchtime? Population Sample(n = 30)

  5. What proportion of NZ Year 5-10 students (mainly) run around at lunch time?

  6. Population What proportion of NZ Year 5-10 pupils (mainly) run around at lunchtime? Sample(n = 30) • The proportion of pupils in my sample who mainly run around during their lunchtime = 0.53 or 53%

  7. Population What proportion of NZ Year 5-10 pupils (mainly) run around at lunchtime? Sample(n = 30) • So, I estimate that about of allYr 5–10 pupils mainly run around during their lunchtime. 0.53 or 53%

  8. What proportion of NZ Year 5-10 pupils (mainly) run around at lunchtime? What did others in the class get for their estimates? I notice that: Everyone seemed to get a different proportion for their sample There was a huge range of sample proportions . . .

  9. Sample 2 (n = 30) Sample 3 (n = 30) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sampling variability Sample 1 (n = 30) Sample Proportions

  10. What proportion of NZ Year 5-10 students (mainly) run around at lunch time?

  11. Sample 2 (n = 30) Sample 3 (n = 30) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sampling variability . . . Sample 1 (n = 30) Sample Proportions

  12. Sample 2 (n = 30) Sample 3 (n = 30) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sampling variability . . . Sample 1 (n = 30) Sample Proportions I notice that: Each sample has different people The sample proportions vary The variability in the sample proportions is large

  13. Sample 2 (n = 30) Sample 3 (n = 30) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sampling variability . . . Sample 1 (n = 30) Sample Proportions ≈ 20% • It is a fairly safe bet that: • any sample proportion will be no further than 20% away from the population proportion

  14. Sample 2 (n = 30) Sample 3 (n = 30) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sampling variability . . . Sample 1 (n = 30) Sample Proportions ≈ 20% • It is a fairly safe bet that: • the population proportion will be no further than 20% away from any sample proportion

  15. Population What proportion of NZ Year 5-10 pupils (mainly) run around at lunchtime? Sample(n = 30) • The proportion of pupils in my sample who mainly run around during their lunchtime = 0.53 or 53%

  16. What proportion of NZ Year 5-10 pupils (mainly) run around at lunchtime? • It’s a fairly safe bet that the proportion of all Yr 5–10 pupils who mainly run around during their lunchtime (i.e., the population proportion) is: • no further than 20% away from my sample proportion of 53% • somewhere between 33% and 73% • 53% with a margin of error of 20% I notice that: This range of possible values for the population proportion is so wide that it is practically useless.

  17. Sample 2 (n = 100) Sample 1 (n = 100) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Different sample sizes . . . Sample Proportions

  18. ≈ 9% Different sample sizes n = 100 0.3 0.35 0.4 0.5 0.55 0.6 0.65 0.7 0.45 Sample Proportions I notice that: It is a fairly safe bet that the population proportion will be no further than 9% away from any sample proportion. (Note: )

  19. Sample 2 (n = 250) Sample 1 (n = 250) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Different sample sizes . . . Sample Proportions

  20. ≈ 6% Different sample sizes n = 250 0.3 0.35 0.4 0.5 0.55 0.6 0.65 0.7 0.45 Sample Proportions I notice that: It is a fairly safe bet that the population proportion will be no further than 6% away from any sample proportion. (Note: )

  21. ≈ 4% Different sample sizes n = 1000 0.3 0.35 0.4 0.5 0.55 0.6 0.65 0.7 0.45 Sample Proportions I notice that: It is a fairly safe bet that the population proportion will be no further than 4% away from any sample proportion. (Note: )

  22. What proportion of NZ Year 5-10 pupils (mainly) run around at lunchtime? Conclusion: It is a fairly safe bet that for a random sample of size n, the population proportion will be no further than from the sample proportion.

  23. n = 250 if I want my sample proportion to be no further than about 0.06 or 6% (= ) away from the population proportion • n = 1000 if I want my sample proportion to be no further than about 0.03 or 3% (= ) away from the population proportion What proportion of NZ Year 5-10 pupils (mainly) run around at lunchtime? • When I use a sample proportion to estimate a population proportion then I should use a sample size, n, of at least:

  24. What proportion of NZ Year 5-10 pupils (mainly) run around at lunchtime? • Randomly select a sample of size n = 1000 pupils from the population of all Yr 5–10 pupils:

  25. What proportion of NZ Year 5-10 pupils (mainly) run around at lunchtime? • 5. Randomly select a sample of size n = 1000 pupils from the population of all Yr 5–10 pupils: • My sample proportion = 0.51 or 51% • With 1000 pupils in my sample, it is a fairly safe bet that my sample proportion is no further than 0.03 or 3% away from the population proportion. It’s a fairly safe bet that between 48% and 54% of all Yr 5–10 pupils mainly run around in their lunchtime.

  26. What proportion of NZ Year 5-10 pupils (mainly) run around at lunchtime? • Summary • Warning • Exercise

  27. Some issues • Sampling / nonsampling errors • ‘Random sample’ versus ‘simple random sample’ • Population size and the margin of error • Is ‘n = 30’ sufficiently large to satisfy underlying theory?

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