S3 June 2014 (R) Q2

EdexcelOld spec7 marksIncludes hypothesis testingChi-Squared Tests

2. A survey asked a random sample of 200 people their age and the main use of their mobile phone.

The results are shown in Table 1 below.

		Main use of their mobile phone
		Internet	Texts	Phone calls
Age	Under 20	27	14	9
	From 20 to 40	32	34	29
	Over 40	15	19	21

Table 1

The data are to be used to test whether or not age and main use of their mobile phone are independent.

Table 2 shows the expected frequencies for each group, assuming people’s age and main use of their mobile phone are independent.

		Main use of their mobile phone
		Internet	Texts	Phone calls
Age	Under 20	18.5	16.75	14.75
	From 20 to 40	35.15	31.825	28.025
	Over 40	20.35	18.425	16.225

Table 2

(a) For users under 20 choosing the Internet as the main use of their mobile phone,

(i) verify that the expected frequency is 18.5

(ii) show that the contribution to the \(\chi^2\) test statistic is 3.91 to 3 significant figures.

(2)

(b) Given that the \(\chi^2\) test statistic for the data is 9.893 to 3 decimal places, test at the 5% level of significance whether or not age and main use of their mobile phone are independent. State your hypotheses clearly. (5)

Scheme	Marks
(i) Expected value \(= \frac{50 \times 74}{200} = 18.5\)	B1 cso
(ii) \(\chi^2\) contribution \(= \frac{(27 - 18.5)^2}{18.5} = 3.905405405 = 3.91\) to 3sfs	B1 cso
	(2)

Mark scheme (b)

Scheme	Marks
\(\mathrm{H_0}\): users age and main mobile phone use are independent/ no association between users age and main mobile phone use \(\mathrm{H_1}\): users age and main mobile phone use are not independent/ some association between users age and main mobile phone use	B1
\(\nu = 4\)	B1
Critical value \(\chi^2 = 9.488\)	B1ft
Test statistic is in critical region therefore significant evidence to reject \(\mathrm{H_0}\) and accept \(\mathrm{H_1}\).	M1
Evidence at 5% level that age and main phone use are not independent.	A1ft
	(5)
	(7 marks)

Notes

3rd B1 ft on their value of \(\nu\)

M1 for attempt to compare test statistic and their critical value

A1 ft on test statistic and critical value but must be comment in context. (A0 if hypotheses are the wrong way around)