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Exam-Style Question on Significance

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

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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.

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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.

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