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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Presentation Transcript
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
• OPTN
• > (F6)
• PROB
• RAND
• Int
• RanInt#(1,1370)
Calculator reminder
• OPTN
• > (F6)
• PROB
• RAN#
• Ran# x 1370 + 1
• Ignore decimals
Analysis
• Plot dot plot on axes
• Note the 5 point summary
• {Minimum, lower quartile, median, upper quartile, maximum}
Analysis
• Repeat three more times to complete 4 sets of 15 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