Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.
Significance A slide presentation showing how to use the chi-squared test to measure significance.
Statistical Significance This video explains numeric and categorical data and helps you gain an understanding of when to apply a t-test or a chi-square test.
First Impressions This activity will collect data about your first impressions of some optical illusions. You can then analyse the data to come to your own conclusions.
t-Test Revision A slide presentation designed to revise the key aspects of Student's t-Test.
Here are some exam-style questions on this statement:
- "A group of students were asked how they get to school each day. The results are shown in the following table" ... more
- "One hundred and sixty students are asked how many portions of fruit or vegetables on average they have per day. The data collected is organized in the following table." ... more
- "Ucayali, a multinational technology company that focuses on e-commerce, has a distribution centre in Camelot. As part of a study into healthy lifestyles, the number of cups of coffee drunk by 420 staff members each day were recorded. Results are shown in the table." ... more
- "The older students from Glee High School are required to follow a two year IB Mathematics course. Data were gathered from a sample of 242 students regarding their choice of course. The following data were recorded." ... more
- "The staff of a shop kept records of who bought smart phones during the month of February one year. They looked at the numbers of phones bought by gender and the size of the screens. This information is shown in the table below; S represents the size of the screen in centimetres." ... more
- "The Scrumptious Sweet Company sell a variety pack of colourful, shaped sweets. The sweets are produced such that 60% are square and 40% are circular. It is known that 20% of the square shaped sweets and 40% of the circular sweets are coloured red." ... more
- "The 2nd Rutherford American Scouts joined the 37th Wolverhampton British Scouts for an International Camp. Skipper Jones is interested to see if the mean height of American Scouts, \( \mu_1\), is the same as the mean height of British Scouts, \( \mu_2\). The information is recorded in the following table." ... more
- "A survey was conducted asking people's opinions on whether mouthwash should be used before or after brushing teeth. The results are shown as follows." ... more
Click on a topic below for suggested lesson Starters, resources and activities from Transum.
- Probability Probability is a measure of the weight of evidence, and is arrived at through reasoning and inference. In simple terms it is a measure or estimation of likelihood of the occurrence of an event. The word probability comes from the Latin word probabilitas which is a measure of the authority of a witness in a legal case. Some of the earlier mathematical studies of probability were motivated by the desire to be more profitable when gambling. Today however the practical uses of probability theory go far beyond gambling and are used in many aspects of modern life. We believe that even adults can, in many cases, have a poor intuition regarding the effects of probability. These activities are designed to help pupils calculate but also get a 'feel' for the principles of probability.
- Statistics Statistics is the study of the collection, organisation, analysis, interpretation and presentation of data. It deals with all aspects of data, including the planning of data collection in terms of the design of surveys and experiments. It also includes describing mathematical relationships between variables and presenting these to an audience in a way that best conveys meaning. See also the topics called Data Handling, Probability and Averages.
Furthermore
The IB AI Syllabus provides the following guidance and clarification:
Hypotheses
Students should express H0 and H1 as an equation or inequality, or in words as appropriate.
Chi-squared Test
- the maximum number of rows or columns in a contingency table will be 4
- the degrees of freedom will always be greater than one. At SL the degrees of freedom for the goodness of fit test will always be n…1
- the 𝜒2 critical value will be given if appropriate
- students will be expected to use technology to find a p -value and the 𝜒2 statistic
- only questions on upper tail tests with commonly-used significance levels (1%, 5%, 10%) will be set
- students will be expected to either compare a p -value to the given significance level or compare the 𝜒2 statistic to a given critical value
- expected frequencies will be greater than 5.
Hand calculations of the expected values or the 𝜒2 statistic may enhance understanding.
If using 𝜒2 tests in the IA, students should be aware of the limitations of the test for expected frequencies of 5 or less.
t-Test
In examinations calculations will be made using technology.
At Standard Level, samples will be unpaired, and population variance will always be unknown.
Students will be asked to interpret the results of a test.
Students should know that the underlying distribution of the variables must be normal for the t-test to be applied. In examinations, students should assume that variance of the two groups is equal and therefore the pooled two-sample t-test should be used.
This Bicen Maths video clip shows everything you need to memorise on hypothesis testing for A Level Statistics.
This Revision Village video clip shows what you need to know on hypothesis testing for the IB AI course.
If you use a TI-Nspire GDC there are instructions useful for this topic.
How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.
