IB Maths AI HL AI 4.4 Hypothesis testing and confidence intervals questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

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Question 1

Paper 1Hard6 marks

A field team measures the nitrate concentration in water samples from a catchment. The eight samples are selected independently at random. Assume that the population of nitrate concentrations is normally distributed, with known standard deviation $1.2\text{ mg L}^{-1}$

Figure 1 shows the measured concentrations. The team will test whether the population mean concentration exceeds $5.0\text{ mg L}^{-1}$ using

H_0:\mu=5.0,\qquad H_1:\mu>5.0,

where $\mu$ is measured in $\text{mg L}^{-1}$

(a)

Use Figure 1 to determine the sample mean concentration.

[1]

(b)

Using your answer to part (a), carry out the stated test at the 5% significance level. State your conclusion in context.

[2]

(c)

Suppose that the true population mean concentration is $5.8\text{ mg L}^{-1}$ Determine the probability of a Type II error for the test in part (b). Give your answer to three significant figures.

[3]

Question 2

Paper 1Hard6 marks

During fieldwork, students randomly selected 50 plots in each of three habitat types and recorded whether a particular plant species was present.

Habitat type	Plant present	Plant absent
Woodland interior	22	28
Woodland edge	35	15
Open scrub	23	27

(a)

State appropriate null and alternative hypotheses for investigating whether plant presence is related to habitat type.

[2]

(b)

Using an appropriate statistical test and your GDC, determine the test statistic, its degrees of freedom and the p-value.

[2]

(c)

At the 5% significance level, state what the data indicate. A volunteer claims that the test proves woodland edge causes a greater probability of plant presence than open scrub. Assess this claim.

[2]

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