Mathematics 9709 · AS & A Level · Hypothesis testing

Hypothesis testing — practice question

A particular type of firework is expected to burn for an average of 30 seconds after being lit. An inspector thinks these fireworks may in fact burn for a shorter average time. He selects a random sample of 100 fireworks of this type. Each firework in the sample is ignited and its duration is recorded. It is known that the population standard deviation of the times that fireworks of this type last is 5 seconds.
(a)[1]

State why a sample has to be taken instead of testing all the fireworks of this type.

(b)[5]

The sample mean for the 100 fireworks is 29 seconds. Test the inspector’s suspicion at the 1\% significance level.

(c)[1]

State, with a reason, whether the Central Limit theorem was needed in the solution to part (b).

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: The fireworks are ruined when they are tested

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