Teachers page: Money for nothing

Curriculum links

NCEA Mathematics Achievement Standard AS90288

• Select a sample and use this to make an inference about the population.

Mathematics and Statistics: Statistics strand – level 7

– Carry out investigations of phenomena, using the statistical enquiry cycle:

• conducting surveys that require random sampling techniques, conducting experiments, and using existing data sets;
•  evaluating the choice of measures for variables and the sampling and data collection methods used;
• using relevant contextual knowledge, exploratory data analysis, and statistical inference.
  – Make inferences from surveys and experiments:
•  making informal predictions, interpolations, and extrapolations;
•  using sample statistics to make point estimates of population parameters;
•  recognising the effect of sample size on the variability of an estimate.

Background

This activity, Money for nothing, focuses on selecting a sample to answer a question, as required by AS90288. The question involves investigating hours worked by employees in a company.

A subset of the database, with only a few variables, is probably more useful. Other variables that could affect hours of work are age and sex so these three are probably the most useful variables.

The answers assume that this subset has been used.
NB. This activity should be modified because data on hours worked is not included. Any of the other continuous variables could be used.

Frequency table for five year age groups

Sample answers

1. Any of the main sampling methods can be justified – simple random, systematic, or stratified on age group (5- or 10- year groups could be used.)

Justification

Simple random or systematic sampling: there are no particular patterns in the dataset and these methods will usually give a representative sample. (Dataset must not be sorted into any particular order if systematic is used). It could be argued that the part timers will be fairly represented because of the randomness of the method.

Stratified sampling: if there is a possible difference in hours worked for different age groups (because of students doing part time work) then a stratified sample based on age group would be useful in ensuring the sample is representative.

1. The random samples should fairly represent age groups. The stratified sample should represent the sex balance.

Frequency table for sex