IB Maths AI HL Ahl 4 16 Hl Confidence Intervals Questions

Practise constructing and interpreting confidence intervals for means using normal or t distributions, selecting degrees of freedom and avoiding overstated certainty.

Exam points

Construct a confidence interval for a normal-population mean using the normal distribution when σ is known.
Use the t-distribution when σ is unknown and select the correct degrees of freedom or technology procedure.
Interpret the confidence level, interval and population parameter in context without overstating certainty.

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Study AHL 4.16 (HL)—Confidence intervals conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 6]

A random sample of eight packets of Apollo coffee granules are selected from a supermarket shelf.
The weights of the coffee granules present in each packet are as follows:
$222 \mathrm{~g} \quad 226 \mathrm{~g} \quad 221 \mathrm{~g} \quad 228 \mathrm{~g} \quad 227 \mathrm{~g} \quad 225 \mathrm{~g} \quad 222 \mathrm{~g} \quad 223 \mathrm{~g}$

(a)

Calculate a 95 % confidence interval for the population mean. Give your answer to four significant figures.

[ 3 ]

[222.1, 226.4]

Note: Award A1 for each correct end of the interval. Accept open or closed (weak or strict) interval notation. Inequalities involving $\mu$ would also be accepted, but not involving $\bar{x}$ .

Award A1A0 for correct answers not given correct to 4 sf.

(b)

State one assumption you have made in order for your interval to be valid.

[ 1 ]

(c)

The label of each packet has a description which includes the phrase: "contains 226 g of coffee granules".

Using your answer to part (a)(ii), briefly comment on the claim on the label.

[ 2 ]

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IB Maths AI HL Ahl 4 16 Hl Confidence Intervals Questions question 1

Question (a)

Question (b)

Question (c)