21M.1.AHL.TZ1.11

pestleMathematicsAIHLPaper 121M· sl-4-1-concepts-reliability-and-sampling-techniques, ahl-4-18-t-and-z-test-type-i-and-ii-errorssource ↗

A factory, producing plastic gifts for a fast food restaurant’s Jolly meals, claims that just $1 %$ of the toys produced are faulty.

A restaurant manager wants to test this claim. A box of $200$ toys is delivered to the restaurant. The manager checks all the toys in this box and four toys are found to be faulty.

The restaurant manager performs a one-tailed hypothesis test, at the $10 %$ significance level, to determine whether the factory’s claim is reasonable. It is known that faults in the toys occur independently.

Identify the type of sampling used by the restaurant manager.

[1]

Write down the null and alternative hypotheses.

[2]

Find the $p$ -value for the test.

[2]

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

[2]

Markscheme / solution

Convenience A1

[1 mark]

$H_{0} :$ $1 %$ of the toys produced are faulty A1

$H_{1} :$ More than $1 %$ are faulty A1

[2 marks]

$X ~ B (200, 0.01)$ (M1)

$P (X \geq 4) = 0.142$ A1

Note: Any attempt using Normal approximation to find $p$ -value is awarded M0A0.

[2 marks]

$14 % > 10 %$ R1

so there is insufficient evidence to reject $H_{0}$ . A1

Note: Do not award R0A1. Accept “fail to reject $H_{0}$ ” or “accept $H_{0}$ ”.

[2 marks]

Examiners’ report

[N/A]