Money for nothing - teachers page

Secondary activity

Money for nothing

Curriculum links

NCEA Mathematics Achievement Standard AS90288  

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

Mathematics: Statistics strand – level 7

• plan a statistical investigation to make inferences about a population or experimental situation
• design and justify sample selection and data collection methods
• collect data, present it visually, and discuss prominent features of the data
• calculate sample statistics, including mean and standard deviation, and verify these by reference to a data distribution.

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 gender so these three are probably the most useful variables.

The answers assume that this subset has been used.

Sample answers

a) Any of the main sampling methods can be justified – simple random, systematic, or stratified on age group (probably 10-year groups would be best).

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.

b) The random samples should fairly represent age groups. The stratified sample should represent the gender balance.