CAIE S2 2014 June — Question 2 5 marks

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2014
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicConfidence intervals
TypeCalculate CI from summary stats
DifficultyModerate -0.3 This is a straightforward application of the confidence interval formula for a mean with large sample size (n=70), requiring only substitution into the standard formula with critical value from normal distribution. The calculation is routine with no conceptual challenges beyond knowing the formula, making it slightly easier than average.
Spec5.05d Confidence intervals: using normal distribution
2 A die is biased. The mean and variance of a random sample of 70 scores on this die are found to be 3.61 and 2.70 respectively. Calculate a \(95 \%\) confidence interval for the population mean score.
Question 2:
AnswerMarks Guidance
Answer/WorkingMark Guidance
\(\frac{70}{69} \times 2.70 = 2.73913\)M1A1
\(3.61 \pm z\sqrt{\frac{"2.73913"}{70}}\)M1 or \(3.61 \pm z\sqrt{\frac{2.70}{69}}\) M2A1(implied)
without \(\frac{70}{69}\): \(3.61 \pm z\sqrt{\frac{2.70}{70}}\) M0A0M1
\(z = 1.96\)B1 \(z = 1.96\) B1
\(3.22\) to \(4.00\) (3 sf)A1 [5] \(3.23\) to \(3.99(4.00)\) (3 sf) A1; Answer must be an interval 
## Question 2:

| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{70}{69} \times 2.70 = 2.73913$ | M1A1 | |
| $3.61 \pm z\sqrt{\frac{"2.73913"}{70}}$ | M1 | or $3.61 \pm z\sqrt{\frac{2.70}{69}}$ M2A1(implied) |
| | | without $\frac{70}{69}$: $3.61 \pm z\sqrt{\frac{2.70}{70}}$ M0A0M1 |
| $z = 1.96$ | B1 | $z = 1.96$ B1 |
| $3.22$ to $4.00$ (3 sf) | A1 [5] | $3.23$ to $3.99(4.00)$ (3 sf) A1; Answer must be an interval |

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2 A die is biased. The mean and variance of a random sample of 70 scores on this die are found to be 3.61 and 2.70 respectively. Calculate a $95 \%$ confidence interval for the population mean score.

\hfill \mbox{\textit{CAIE S2 2014 Q2 [5]}}
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