CAIE S2 2002 November — Question 1 3 marks

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2002
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicConfidence intervals
TypeCalculate CI from summary stats
DifficultyModerate -0.8 This is a straightforward confidence interval calculation requiring only direct substitution into the standard formula with given values (sample mean, variance, and sample size). The large sample size (n=120) means students can use the normal distribution without concern, and all necessary information is provided explicitly. This is simpler than average A-level questions as it involves no problem-solving, just mechanical application of a memorized procedure.
Spec5.05d Confidence intervals: using normal distribution

The time taken, \(T\) minutes, for a special anti-rust paint to dry was measured for a random sample of 120 painted pieces of metal. The sample mean was 51.2 minutes and an unbiased estimate of the population variance was 37.4 minutes\(^2\). Determine a 99% confidence interval for the mean drying time. [3]

AnswerMarks Guidance
\(512 \pm 2.576 \times \frac{37.4}{120}\) giving \(49.8 < \mu < 52.6\)M1, B1, A1 (3 marks) Calculation of correct form. Using \(z = 2.576\) or equivalent statement.
$512 \pm 2.576 \times \frac{37.4}{120}$ giving $49.8 < \mu < 52.6$ | M1, B1, A1 (3 marks) | Calculation of correct form. Using $z = 2.576$ or equivalent statement.

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The time taken, $T$ minutes, for a special anti-rust paint to dry was measured for a random sample of 120 painted pieces of metal. The sample mean was 51.2 minutes and an unbiased estimate of the population variance was 37.4 minutes$^2$. Determine a 99% confidence interval for the mean drying time. [3]

\hfill \mbox{\textit{CAIE S2 2002 Q1 [3]}}