Using a sample to make a point estimate
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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

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Using a sample to make a point estimate

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Using a sample to make a point estimate

Using a sample to make a point estimate

Stage 1 Statistics students from Auckland university


Stage 1 statistics data

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.


Variables recorded

Variables recorded


Reminder ppdac cycle

Reminder – PPDAC cycle…


Problem

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

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

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.


Using a sample to make a point estimate

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.


Using a sample to make a point estimate

Data

  • SRS of 15 students

  • Make sure you don’t sample the same student more than once


Calculator reminder

Calculator reminder

  • Run menu

  • OPTN

  • > (F6)

  • PROB

  • RAND

  • Int

  • RanInt#(1,1370)


Calculator reminder1

Calculator reminder

  • Run menu

  • OPTN

  • > (F6)

  • PROB

  • RAN#

  • Ran# x 1370 + 1

  • Ignore decimals


Analysis

Analysis

  • Plot dot plot on axes

  • Add box plot above

  • Note the 5 point summary

    • {Minimum, lower quartile, median, upper quartile, maximum}


Analysis1

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

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….


Conclusion1

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

Everyone’s plots

  • What do you notice?


Everyone s plots1

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 plots2

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

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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