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Using a sample to make a point estimate

Stage 1 Statistics students from Auckland university

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.

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?

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

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.

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.

Data

- SRS of 15 students
- Make sure you don’t sample the same student more than once

Calculator reminder

- Run menu
- OPTN
- > (F6)
- PROB
- RAND
- Int
- RanInt#(1,1370)

Calculator reminder

- Run menu
- OPTN
- > (F6)
- PROB
- RAN#
- Ran# x 1370 + 1
- Ignore decimals

Analysis

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

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…

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….

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….

Everyone’s plots

- What do you notice?

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

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

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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