(a(i))[3]
Calculate the value of $\sigma$.
(a(ii))[3]
Carry out the hypothesis test at the $2.5\%$ significance level.
(b)[1]
Explain whether it was necessary to use the Central Limit Theorem in carrying out the test.
Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
The pencil lengths produced in a factory are normally distributed. Their standard deviation is $\sigma$ cm, and the intended mean length is $10$ cm. An inspector suspects that the true mean exceeds $10$ cm. He selects a random sample of $50$ pencils from the factory and obtains a sample mean of $10.03$ cm. He then carries out a hypothesis test and finds that the test statistic $z$ has value $1.995$ correct to $3$ decimal places.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Set up standardised test statistic $\frac{10.03-10}{\sigma/\sqrt{50}}=1.995$” …
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