Solved: A group of 1280 students were asked which electronic device they preferred. The... [IB Mathematics Applications & Interpretation (Math AI)]

Question

SLPaper 2

A group of 1280 students were asked which electronic device they preferred. The results per age group are given in the following table.

	Age
Preferred device	11-13	14-16	17-18	Total
Laptop	143	160	153	456
Tablet	205	224	131	560
Mobile phone	72	128	64	264
Total	420	512	348	1280

A student from the group is chosen at random. Calculate the probability that the student prefers a tablet.

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Solution

Note: Award A1 for correct numerator, A1 for correct denominator. $\frac{560}{1280}$ ( $\frac{7}{16}$ , 0.4375)

A student from the group is chosen at random. Calculate the probability that the student is 11-13 years old and prefers a mobile phone.

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Solution

Note: Award A1 for correct numerator, A1 for correct denominator. $\frac{72}{1280}$ ( $\frac{9}{160}$ , 0.05625)

A student from the group is chosen at random. Calculate the probability that the student prefers a laptop given that they are 17-18 years old.

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Solution

Note: Award A1 for correct numerator, A1 for correct denominator. $\frac{153}{348}$ ( $\frac{51}{116}$ , 0.439655...) A1A1

A student from the group is chosen at random. Calculate the probability that the student prefers a tablet or is 14-16 years old.

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Solution

Note: Award A1 for correct denominator (1280) seen, (M1) for correct calculation of the numerator, A1 for the correct answer. $160+224+128+205+131$ OR $560+512-224$ $\frac{848}{1280}$ ( $\frac{53}{80}$ , 0.6625)

State the null and alternative hypotheses.

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Solution

Write down the number of degrees of freedom.

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Solution

Write down the χ² test statistic.

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Solution

( $\chi^2 =$ ) 23.3 (23.3258...)

Write down the p-value.

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Solution

0.000109 (0.000108991...) OR $1.09 \times 10^{-4}$

State the conclusion for the test in context. Give a reason for your answer.

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Solution

EITHER $23.3 > 13.277$ R1 OR $0.000109 < 0.01$ R1

THEN (there is sufficient evidence to accept $H_1$ that) preferred device and age group are not independent A1R1 Note: For the final A1 the answer must be in context. Do not award A1R0.

A group of 1280 students were asked which electronic device they preferred. The results per age group are given in the following table.

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