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.

Observed quadrat frequenciesNumber of quadrats051015202530ABCHabitat typeMoths detectedNo moths detected
(a)

State the null hypothesis, H0H_0 and the alternative hypothesis, H1H_1 for a test of whether moth detection and habitat type are independent.

[2]
(b)

Assuming H0H_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 χ2\chi^2 statistic and the pp-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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