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Date November 2017 Marks available 2 Reference code 17N.2.SL.TZ0.T_1
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Find Question number T_1 Adapted from N/A

Question

A group of 800 students answered 40 questions on a category of their choice out of History, Science and Literature.

For each student the category and the number of correct answers, N , was recorded. The results obtained are represented in the following table.

N17/5/MATSD/SP2/ENG/TZ0/01

A χ 2 test at the 5% significance level is carried out on the results. The critical value for this test is 12.592.

State whether N is a discrete or a continuous variable.

[1]
a.

Write down, for N , the modal class;

[1]
b.i.

Write down, for N , the mid-interval value of the modal class.

[1]
b.ii.

Use your graphic display calculator to estimate the mean of N ;

[2]
c.i.

Use your graphic display calculator to estimate the standard deviation of N .

[1]
c.ii.

Find the expected frequency of students choosing the Science category and obtaining 31 to 40 correct answers.

[2]
d.

Write down the null hypothesis for this test;

[1]
e.i.

Write down the number of degrees of freedom.

[1]
e.ii.

Write down the p -value for the test;

[1]
f.i.

Write down the χ 2 statistic.

[2]
f.ii.

State the result of the test. Give a reason for your answer.

[2]
g.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

discrete     (A1)

[1 mark]

a.

11 N 20     (A1)

[1 mark]

b.i.

15.5     (A1)(ft)

 

Note:     Follow through from part (b)(i).

 

[1 mark]

b.ii.

21.2   ( 21.2125 )     (G2)

[2 marks]

c.i.

9.60   ( 9.60428 )     (G1)

[1 marks]

c.ii.

260 800 × 157 800 × 800 OR 260 × 157 800     (M1)

 

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

 

= 51.0   ( 51.025 )     (A1)(G2)

[2 marks]

d.

choice of category and number of correct answers are independent     (A1)

 

Notes:     Accept “no association” between (choice of) category and number of correct answers. Do not accept “not related” or “not correlated” or “influenced”.

 

[1 mark]

e.i.

6     (A1)

[1 mark]

 

e.ii.

0.0644   ( 0.0644123 )     (G1)

[1 mark]

f.i.

11.9   ( 11.8924 )     (G2)

[2 marks]

f.ii.

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

OR

(choice of) category and number of correct answers are independent     (A1)(ft)

as 11.9 < 12.592 OR 0.0644 > 0.05     (R1)

 

Notes:     Award (R1) for a correct comparison of either their χ 2 statistic to the χ 2 critical value or their p -value to the significance level. Award (A1)(ft) from that comparison.

Follow through from part (f). Do not award (A1)(ft)(R0).

 

[2 marks]

g.

Examiners report

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

Syllabus sections

Topic 4—Statistics and probability » SL 4.2—Histograms, CF graphs, box plots
Show 122 related questions
Topic 4—Statistics and probability » SL 4.3—Mean, median, mode. Mean of grouped data, standard deviation. Quartiles, IQR
Topic 4—Statistics and probability

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