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Date November 2019 Marks available 2 Reference code 19N.2.SL.TZ0.T_1
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Calculate Question number T_1 Adapted from N/A

Question

Casanova restaurant offers a set menu where a customer chooses one of the following meals: pasta, fish or shrimp.

The manager surveyed 150 customers and recorded the customer’s age and chosen meal. The data is shown in the following table.

A χ2 test was performed at the 10% significance level. The critical value for this test is 4.605.

Write down

A customer is selected at random.

State H0, the null hypothesis for this test.

[1]
a.

Write down the number of degrees of freedom.

[1]
b.

Show that the expected number of children who chose shrimp is 31, correct to two significant figures.

[2]
c.

the χ2 statistic.

[2]
d.i.

the p-value.

[1]
d.ii.

State the conclusion for this test. Give a reason for your answer.

[2]
e.

Calculate the probability that the customer is an adult.

[2]
f.i.

Calculate the probability that the customer is an adult or that the customer chose shrimp.

[2]
f.ii.

Given that the customer is a child, calculate the probability that they chose pasta or fish.

[2]
f.iii.

Markscheme

H0 : choice of meal is independent of age (or equivalent)        (A1)

Note: Accept "not associated" or "not dependent" instead of independent. In lieu of "age", accept an equivalent alternative such as "being a child or adult".

[1 mark]

a.

2        (A1)

[1 mark]

b.

69150×67150×150  OR  69×67150  (M1)

Note: Award (M1) for correct substitution into expected frequency formula.

30.82  30.8        (A1)

31        (AG)

Note: Both an unrounded answer that rounds to the given answer and rounded answer must be seen for the (A1) to be awarded.

[2 marks]

c.

χcalc2= 2.66  2.657537         (G2)

[2 marks]

d.i.

(p-value =0.265 0.264803      (G1)

Note: Award (G0)(G2) if the χ2 statistic is missing or incorrect and the p-value is correct.

[1 mark]

d.ii.

0.265>0.10  OR  2.66<4.605        (R1)(ft)

the null hypothesis is not rejected        (A1)(ft)

OR

the choice of meal is independent of age (or equivalent)        (A1)(ft)

Note: Award (R1)(ft)) for a correct comparison of either their χ2 statistic to the χ2 critical value or their p-value to the significance level.
Condone “accept” in place of “not reject”.
Follow through from parts (a) and (d).

Do not award (A1)(ft)(R0).

[2 marks]

e.

81150 2750, 0.54, 54%        (A1)(A1)(G2)

Note: Award (A1) for numerator, (A1) for denominator.

[2 marks]

f.i.

116150 5875, 0.773, 0.773333, 77.3%        (A1)(A1)(G2)

Note: Award (A1) for numerator, (A1) for denominator.

[2 marks]

f.ii.

3469 0.493, 0.492753, 49.3%        (A1)(A1)(G2)

Note: Award (A1) for numerator, (A1) for denominator.

[2 marks]

f.iii.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.i.
[N/A]
d.ii.
[N/A]
e.
[N/A]
f.i.
[N/A]
f.ii.
[N/A]
f.iii.

Syllabus sections

Topic 4—Statistics and probability » SL 4.2—Histograms, CF graphs, box plots
Show 109 related questions
Topic 4—Statistics and probability » SL 4.5—Probability concepts, expected numbers
Topic 4—Statistics and probability » SL 4.6—Combined, mutually exclusive, conditional, independence, prob diagrams
Topic 4—Statistics and probability » SL 4.11—Expected, observed, hypotheses, chi squared, gof, t-test
Topic 4—Statistics and probability

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