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Sample Data Analysis in Statistics Education: Making Effective Point Estimates Using a Sample

Explore the process of making point estimates by analyzing sample data from Stage 1 Statistics students at Auckland University. Learn how to formulate questions, gather data through surveys, analyze and compare subsets of data, interpret distributions, and understand sampling errors in statistics education.

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Sample Data Analysis in Statistics Education: Making Effective Point Estimates Using a Sample

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  1. Using a sample to make a point estimate Stage 1 Statistics students from Auckland university

  2. 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.

  3. Variables recorded

  4. Reminder – PPDAC cycle…

  5. Problem • What sort of question is this? • How would we have worded this question last year? (Level 1) • What other sort of investigative questions are there? • What makes a good question? • I wonder what the median weight of Stage 1 Statistics students at Auckland University is?

  6. Reminders… Question types Good questions • SUMMARY • Description of one variable • COMPARISON • Comparing two (or more) subsets of data across a common numeric variable • RELATIONSHIP • Looking at the interrelationship between two paired numeric variables • Can be answered with the data • Population of interest is clear • Variable(s) of interest is clear • Intent (summary, comparison, relationship) is clear • Someone is interested in the answer

  7. I wonder what the median weight of Stage 1 Statistics students at Auckland University is? • What do you think the median weight will be? • Why? • Sketch the shape of the distribution of weights of Stage 1 Statistics students from Auckland University.

  8. Plan • What variable are we going to use to answer our question? • How are we going to gather our data? • Everyone? • Sample? • Simple random sample of 15 students please.

  9. Data • SRS of 15 students • Make sure you don’t sample the same student more than once

  10. Calculator reminder • Run menu • OPTN • > (F6) • PROB • RAND • Int • RanInt#(1,1370)

  11. Calculator reminder • Run menu • OPTN • > (F6) • PROB • RAN# • Ran# x 1370 + 1 • Ignore decimals

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

  13. Analysis • Repeat three more times to complete 4 sets of 15 samples • Write (at least) three “I notice…” statements about your samples • Look at shape and spread – what do you notice? • Similarities? Differences? – between your sets of samples…

  14. Conclusion Use sample median to provide a point estimate of the population parameter • From my sample data I estimate that the median weight for all Stage 1 statistics students at Auckland University is….

  15. Conclusion • But they’re all different! • Who is right? • From my sample data I estimate that the median weight for all Stage 1 statistics students at Auckland University is….

  16. Everyone’s plots • What do you notice?

  17. Everyone’s plots • What do you notice? • Samples are all different • All centred (clustered) around the same values • Mostly skewed to the right • Medians fall within a band, an interval

  18. Everyone’s plots • How can we use our sample to predict what is going on back in the population? • The sample median is our best idea of the population median

  19. Sampling error • The process of taking a sample and using the median of the sample to predict the population median will never produce the exact value of the population median. • This is called sampling error • The difference between the sample median and the true value back in the population

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