## Exam-Style Question on Significance## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 463. This question is similar to one that appeared on an IB AI Standard paper (specimen) for 2021. The use of a calculator is allowed.

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.

(a) Show this information in a tree diagram.

A sweet is selected at random.

(b) Find the probability that the sweet is red.

(c) Given that the sweet is red, find the probability it is circular.

The Scrumptious Sweet Company also produce variety packs of Rainbow Gums. Their specifications state that the colours in each variety pack should be distributed as follows.

Colour | Red | Orange | Yellow | Green | Blue |

Percentage (%) | 15 | 25 | 15 | 25 | 20 |

Inspector Lou Spowels opens a pack of 90 sweets and records the frequency of each colour:

Colour | Red | Orange | Yellow | Green | Blue |

Observed Frequency | 12 | 21 | 15 | 20 | 22 |

To investigate if the sample is consistent with the company's specifications, Mr Spowels conducts a \(\chi^2\) goodness of fit test. The test is carried out at a 5% significance level.

(d) Write down the null hypothesis for this test.

(e) Copy and complete the following table giving the frequencies correct to one decimal place:

Colour | Red | Orange | Yellow | Green | Blue |

Expected Frequency |

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

(g) Find the p-value for the test.

(h) State the conclusion of the test. Give a reason for your answer.

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 need more practice try the self-checking interactive exercises called Tree Diagrams. There is also a slide presentation you might find useful on the Chi squared GOF test.

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

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 - 2021 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/