IB Mathematics Applications & Interpretation Topic AHL 4.16—confidence Intervals Questionbank (HL)

IB Mathematics Applications & Interpretation Topic AHL 4.16—confidence Intervals Questionbank (HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic AHL 4.16—confidence Intervals with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 4.16—confidence Intervals and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

HLPaper 2

A factory seals tea in foil sachets. The mass of tea in a sachet has population mean $μ$ g and variance $1.44$ . Independent random samples of size $n = 64$ are taken.

The quality team suspects underfilling and tests $H_{0} : μ = 7.5$ against $H_{1} : μ < 7.5$ at a significance level of $2.5%$ using a sample of 64 sachets.

Define the Central Limit Theorem for the sample mean of a random sample of size $n$ drawn from a population with mean $μ$ and variance $σ^{2}$ .

[2]

A sample of 64 sachets gives a mean mass of $\overset{x}{ˉ} = 7.32$ . Determine a 90% confidence interval for the population mean $μ$ .

[2]

Calculate the critical region for the quality team's hypothesis test, rounding your value to two decimal places.

[4]

State the likelihood that the quality team commits a Type I error.

[1]

If the probability of committing a Type II error is $0.10$ , determine the specific value of $μ$ , correct to three significant figures.

[5]

Question 2

HLPaper 2

A researcher is studying the effect of a new fertilizer on plant growth. In a sample of $30$ plants, the mean increase in height is $15$ cm and the variance calculated using denominator $n$ is $9 cm^{2}$ .

Find the unbiased estimate of the population variance.

[2]

Find a $99%$ confidence interval for the mean increase in height of the plants, stating any assumptions you make.

[3]

The researcher claims that the fertilizer increases plant height by more than $17$ cm on average. Comment on this claim in the light of your confidence interval.

[2]

Question 3

HLPaper 1

Dispensing volumes for a café syrup pump are assumed to be normally distributed. A random sample of 10 drinks gives a mean syrup volume of 18.7 ml and a standard deviation of 1.5 ml calculated using divisor $n$ , so $s_{n} = 1.5$ .

Calculate the unbiased estimate of the population standard deviation, $s_{n - 1}$ , for these data.

[2]

Determine a 95 % confidence interval for the true mean syrup volume, presenting your result to 4 significant figures.

[2]

The manager claims that the mean syrup volume is 20 ml. Evaluate this claim using your confidence interval.

[1]

Question 4

HLPaper 1

A sample of 10 delivery times, in minutes, for a local courier service is: $41, 43, 45, 46, 48, 52, 54, 55, 57, 59$ .

Find the $90%$ confidence interval for the population mean, $μ$ , using the sample standard deviation.

[4]

If the population standard deviation is $σ = 6$ , find the $90%$ confidence interval for $μ$ .

[2]

Compare the widths of the two confidence intervals.

[2]

Question 5

HLPaper 1

A random sample of 36 rechargeable batteries is tested for operating time, yielding a sample mean of $\overset{x}{ˉ} = 12.6 h$ and a sample variance of $s_{n - 1}^{2} = 3.24 (h)^{2}$ . Assume the operating times are normally distributed.

Find a $90%$ confidence interval for the population mean operating time, $μ$ .

[3]

Sketch the confidence interval on a number line.

[3]

The company claims the mean operating time is $13 h$ . Based on the confidence interval, comment on the validity of this claim.

[2]

State the Central Limit Theorem as it applies to this context.

[1]

IB Mathematics Applications & Interpretation AHL 4.16—confidence Intervals Questionbank

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IB Mathematics Applications & Interpretation AHL 4.16—confidence Intervals Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 4.16—confidence Intervals Questionbank

Unlock all 25 questions with a free account