AQA S2 2008 June — Question 3 6 marks

Exam BoardAQA
ModuleS2 (Statistics 2)
Year2008
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicZ-tests (known variance)
TypeTwo-tail z-test
DifficultyModerate -0.3 This is a straightforward one-sample z-test with all information clearly provided (known variance, sample size, sample mean, significance level). Students need only apply the standard hypothesis testing procedure with no conceptual challenges or multi-step reasoning—slightly easier than average due to its routine nature and clear setup.
Spec5.05c Hypothesis test: normal distribution for population mean

3 Alan's company produces packets of crisps. The standard deviation of the weight of a packet of crisps is known to be 2.5 grams. Alan believes that, due to the extra demand on the production line at a busy time of the year, the mean weight of packets of crisps is not equal to the target weight of 34.5 grams. In an experiment set up to investigate Alan's belief, the weights of a random sample of 50 packets of crisps were recorded. The mean weight of this sample is 35.1 grams. Investigate Alan's belief at the \(5 \%\) level of significance.

Question 3:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(H_0: \mu = 34.5\); \(H_1: \mu \neq 34.5\)B1
\(z_{\text{crit}} = \pm 1.96\)B1
\(z = \frac{35.1 - 34.5}{\frac{2.5}{\sqrt{50}}} = 1.70\)M1A1 (1.697)
Accept \(H_0\)A1
Insufficient evidence, at 5% level of significance, to suggest that the mean weight has changedE1 6 marks total; or … to confirm Alan's belief
## Question 3:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $H_0: \mu = 34.5$; $H_1: \mu \neq 34.5$ | B1 | |
| $z_{\text{crit}} = \pm 1.96$ | B1 | |
| $z = \frac{35.1 - 34.5}{\frac{2.5}{\sqrt{50}}} = 1.70$ | M1A1 | (1.697) |
| Accept $H_0$ | A1 | |
| Insufficient evidence, at 5% level of significance, to suggest that the mean weight has changed | E1 | 6 marks total; or … to confirm Alan's belief |

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3 Alan's company produces packets of crisps. The standard deviation of the weight of a packet of crisps is known to be 2.5 grams.

Alan believes that, due to the extra demand on the production line at a busy time of the year, the mean weight of packets of crisps is not equal to the target weight of 34.5 grams.

In an experiment set up to investigate Alan's belief, the weights of a random sample of 50 packets of crisps were recorded. The mean weight of this sample is 35.1 grams.

Investigate Alan's belief at the $5 \%$ level of significance.

\hfill \mbox{\textit{AQA S2 2008 Q3 [6]}}