Moderate -0.3 This is a straightforward two-tail z-test with given population standard deviation. Students must calculate the sample mean, apply the z-test formula, and compare to critical values. While it requires multiple steps (5 marks typical), it's a standard textbook procedure with no conceptual challenges—slightly easier than average due to being a direct application of a learned method with clear structure.
2 The times taken by students to complete a task are normally distributed with standard deviation 2.4 minutes. A lecturer claims that the mean time is 17.0 minutes. The times taken by a random sample of 5 students were 17.8, 22.4, 16.3, 23.1 and 11.4 minutes. Carry out a hypothesis test at the \(5 \%\) significance level to determine whether the lecturer's claim should be accepted.
Allow incorrect 18.2. Must have \(\sqrt{5}\). Alt: \(17 \pm 1.96\dfrac{2.4}{\sqrt{5}}\) M1 \(= (14.9, 19.1)\) A1
\(1.12 < 1.96\) oe
M1
Compare \(1.12\) with 1.96 or area \(0.132\) with 0.025. Alt: \(14.9 < 18.2 < 19.1\) M1
Claim can be accepted
A1ft [5]
ft their \(1.12\). If \(H_1: \mu > 17\) and cf 1.645: can score max B0M1A1M1A1ft
## Question 2:
| Answer | Mark | Guidance |
|--------|------|----------|
| $H_0$: Pop mean $= 17$; $H_1$: Pop mean $\neq 17$ | B1 | Both correct. Allow $\mu$, but not just "mean" |
| $\dfrac{18.2 - 17}{\dfrac{2.4}{\sqrt{5}}} = 1.12$ (3 sf) | M1, A1 | Allow incorrect 18.2. Must have $\sqrt{5}$. Alt: $17 \pm 1.96\dfrac{2.4}{\sqrt{5}}$ M1 $= (14.9, 19.1)$ A1 |
| $1.12 < 1.96$ oe | M1 | Compare $1.12$ with 1.96 or area $0.132$ with 0.025. Alt: $14.9 < 18.2 < 19.1$ M1 |
| Claim can be accepted | A1ft [5] | ft their $1.12$. If $H_1: \mu > 17$ and cf 1.645: can score max B0M1A1M1A1ft |
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2 The times taken by students to complete a task are normally distributed with standard deviation 2.4 minutes. A lecturer claims that the mean time is 17.0 minutes. The times taken by a random sample of 5 students were 17.8, 22.4, 16.3, 23.1 and 11.4 minutes. Carry out a hypothesis test at the $5 \%$ significance level to determine whether the lecturer's claim should be accepted.
\hfill \mbox{\textit{CAIE S2 2013 Q2 [5]}}