CAIE A-Level Further Math A2 4.2.4 Mean Confidence Intervals Questions

Practise constructing and interpreting confidence intervals for population means, including assumptions that make intervals valid, using Further Mathematics AS questions and mark…

Exam points

Construct and interpret confidence intervals for population means from sample data.

[Maximum number: 4]

Nassa is researching the lengths of a particular type of snake in two countries, A and B.

He takes a random sample of 10 snakes of this type from country A and measures the length, $x \mathrm{~m}$ , of each snake. He then calculates a 90% confidence interval for the population mean length, $\mu \mathrm{m}$ , for snakes of this type, assuming that snake lengths have a normal distribution. This confidence interval is $3.36 \leqslant \mu \leqslant 4.22$ .

Find the sample mean and an unbiased estimate for the population variance.

$\bar{x}=\frac{1}{2}(4.22+3.36)=3.79$ $4.22-3.36=\frac{2 t s}{\sqrt{10}}$

М1

Using z value implies M0

With t=1.833
( s=0.7418 ) variance =0.55(0)
4

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CAIE A-Level Further Math A2 4.2.4 Mean Confidence Intervals Questions question 1