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

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

Reminder – PPDAC cycle…

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 typesGood 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  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