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Date November 2014 Marks available 2 Reference code 14N.1.sl.TZ0.10
Level SL only Paper 1 Time zone TZ0
Command term Calculate Question number 10 Adapted from N/A

Question

Minta surveyed students from her school about their preferred morning snack from a choice of an apple, a fruit salad or a smoothie.

She surveyed 350 students, of whom 210 are female.

She performed a \({\chi ^2}\) test at the 5% significance level to determine whether there is a relationship between the choice of morning snack and gender.

State Minta’s null hypothesis.

[1]
a.

State the number of degrees of freedom.

[1]
b.

150 students showed a preference for a smoothie.

Calculate the expected number of female students who chose a smoothie.

[2]
c.

Minta found that the calculated value of the \({\chi ^2}\) test was 3.576. The critical value at the 5% significance level is \(5.99\).

State Minta’s conclusion. Give a reason for your answer.

[2]
d.

Markscheme

\({{\text{H}}_0}\): Choice of morning snack is independent of (not dependent on) gender.     (A1)     (C1)

Note: Accept there is “no association” between snack chosen and gender.

Do not accept “not related” or “not correlated” or “influenced”.

a.

\(2\)     (A1)     (C1)

b.

\(\frac{{210 \times 150}}{{350}}\)     (M1)

Note: Award (M1) for correct substitution in the correct formula.

 

\( = 90\)     (A1)     (C2)

c.

Null hypothesis is accepted (not rejected).     (A1)

 

OR

Choice of morning snack is independent of gender     (A1)

\(3.576 < 5.99\;\;\;{\mathbf{OR}}\;\;\;\chi _{{\text{calc}}}^2 < \chi _{{\text{crit}}}^2\)     (R1)     (C2)

Note: Do not award (A1)(R0).

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.

Syllabus sections

Topic 4 - Statistical applications » 4.4 » The \({\chi ^2}\) test for independence: formulation of null and alternative hypotheses; significance levels; contingency tables; expected frequencies; degrees of freedom; \(p\)-values.
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