using a sample to make a point estimate

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