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

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Question 1

Paper 1Medium6 marks

During fieldwork, 40 quadrats were examined in each of three habitat types. In each quadrat, the fieldworkers recorded whether moths were detected. Figure 1 shows their results.

(a)

State the null hypothesis, $H_0$ and the alternative hypothesis, $H_1$ for a test of whether moth detection and habitat type are independent.

[2]

(b)

Assuming $H_0$ is true, calculate the expected frequency of quadrats in habitat B in which moths are detected. Give your answer to 3 significant figures.

[1]

(c)

Use a GDC to carry out an appropriate test of independence using the frequencies in Figure 1. Give the $\chi^2$ statistic and the $p$ -value, each to 3 significant figures.

[2]

(d)

Hence state the conclusion of the test at the 5% significance level, in the context of the fieldwork.

[1]

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