AQA S2 2010 January — Question 1 5 marks

Exam BoardAQA
ModuleS2 (Statistics 2)
Year2010
SessionJanuary
Marks5
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Mark schemeDownload PDF ↗
TopicZ-tests (known variance)
TypeOne-tail z-test (upper tail)
DifficultyModerate -0.3 This is a straightforward one-sample hypothesis test with all values provided and a standard procedure to follow. While it requires knowing the z-test method and critical values, it's a routine textbook application with no conceptual subtleties—slightly easier than average because the setup is clear and the calculation is mechanical.
Spec5.05c Hypothesis test: normal distribution for population mean
1 Roger claims that, on average, his journey time from home to work each day is greater than 45 minutes. The times, \(x\) minutes, of 30 randomly selected journeys result in \(\bar { x } = 45.8\) and \(s ^ { 2 } = 4.8\).
Investigate Roger's claim at the \(1 \%\) level of significance.
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(H_0: \mu = 45\), \(H_1: \mu > 45\)B1
\(z = \frac{45.8 - 45}{\sqrt{4.8/30}} = \frac{0.8}{0.4} = 2.0\)M1A1 AWRT
\(z_{\text{crit}} = 2.3263\)B1 \(t_{29} = 2.462\)
Do not reject \(H_0\); insufficient evidence at 1% level of significance to support Roger's claimE1 
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $H_0: \mu = 45$, $H_1: \mu > 45$ | B1 | |
| $z = \frac{45.8 - 45}{\sqrt{4.8/30}} = \frac{0.8}{0.4} = 2.0$ | M1A1 | AWRT |
| $z_{\text{crit}} = 2.3263$ | B1 | $t_{29} = 2.462$ |
| Do not reject $H_0$; insufficient evidence at 1% level of significance to support Roger's claim | E1 | |

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1 Roger claims that, on average, his journey time from home to work each day is greater than 45 minutes.

The times, $x$ minutes, of 30 randomly selected journeys result in $\bar { x } = 45.8$ and $s ^ { 2 } = 4.8$.\\
Investigate Roger's claim at the $1 \%$ level of significance.

\hfill \mbox{\textit{AQA S2 2010 Q1 [5]}}
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Q1 5 Q2 5 Q3 7 Q4 10 Q5 10 Q6 10 Q7 10 Q8 18