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 - PowerPoint PPT PresentationTRANSCRIPT
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
COURSE
The three Stage 1 statistics courses offered at the University of Auckland: Commerce, for students of commerce (49%) General, a General Education paper (two courses
needed for undergraduate degree (3%) Introduction, towards all other degrees, eg psychology,
social science, science (48%)SEX Male (47%)or female (53%)WEIGHTACTUAL Actual weight in KgWEIGHTIDEAL Ideal weight in KgSPEED Maximum speed driven as a licensed driverDRINKSPEND Amount in $ spent on alcohol per week on averageLOOKS Personal appearance rating out of 10INTELLIGENCE Personal intelligence rating out of 10SHOES Number of pairs of shoes ownedHOURSWORKED Number of hours worked per weekWEEKLYWAGE Amount in $ earned per weekVOTE Political party currently supported
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 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