Transum Software

Exam-Style Question on Significance

A mathematics exam-style question with a worked solution that can be revealed gradually

List Of Questions Exam-Style Question More Significance Questions Other Topics

Question id: 205. This question is similar to one that appeared on an IB Studies paper in 2015. The use of a calculator is allowed.

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.

Age below 18Age 18 to 30Age over 30Total

A \(\chi ^2\) test at the 1% significance level was conducted.

(a) State \(H_0\), the null hypothesis for the test;

(b) State \(H_1\), the alternative hypothesis for the test.

(c) Write down the number of degrees of freedom.

(d) Find the expected frequency of people between the age 18 to 30 who believe that mouthwash should be used before brushing.

(e) Find the \(\chi ^2\) statistic;

(f) Find the associated p-value for the test.

(g) Determine, giving a reason, whether \(H_0\) should be accepted.

The worked solutions to these exam-style questions are only available to those who have a Transum Subscription.

Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves.

This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures.

A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.



Drag this panel down to reveal the solution

If you are using a TI-nSpire CX calculator and you would like to see an example of the process used in this question see GDC Essentials.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.


Exam-Style Questions Main Page


Search for exam-style questions containing a particular word or phrase:

To search the entire Transum website use the search box in the grey area below.


Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


©1997-2023 WWW.TRANSUM.ORG

©1997 - 2023 Transum Mathematics :: For more exam-style questions and worked solutions go to