Problem Bank | IB Math AIHL

[Maximum mark: 8]

A toy company advertises that the types of mini-figures found in its cereal packets occur in the following long-run proportions:

Figure type	Robot	Wizard	Athlete	Alien
Claimed proportion	0.25	0.30	0.25	0.20

A random sample of 160 packets is opened, giving the observed frequencies:

Figure type	Robot	Wizard	Athlete	Alien	Total
Observed frequency	46	42	40	32	160

State the null hypothesis H0 and the alternative hypothesis H1 for a χ2 goodness-of-fit test on the data.
[2]
Copy the table below and complete the expected-frequency row, correct to the nearest integer.
Figure type
Robot
Wizard
Athlete
Alien
Expected frequency

[2]
Determine
1. the value of the χ2 test statistic.
  [1]
2. the p-value of the test.
  [1]
At the 5% significance level, state with a reason whether the company’s claim should be rejected.
[2]

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