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Date May Example question Marks available 1 Reference code EXM.2.SL.TZ0.5
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term State Question number 5 Adapted from N/A

Question

A pharmaceutical company has developed a new drug to decrease cholesterol. The final stage of testing the new drug is to compare it to their current drug. They have 150 volunteers, all recently diagnosed with high cholesterol, from which they want to select a sample of size 18. They require as close as possible 20% of the sample to be below the age of 30, 30% to be between the ages of 30 and 50 and 50% to be over the age of 50.

Half of the 18 volunteers are given the current drug and half are given the new drug. After six months each volunteer has their cholesterol level measured and the decrease during the six months is shown in the table.

Calculate the mean decrease in cholesterol for

The company uses a t-test, at the 1% significance level, to determine if the new drug is more effective at decreasing cholesterol.

State the name for this type of sampling technique.

[1]
a.

Calculate the number of volunteers in the sample under the age of 30.

[3]
b.

The new drug.

[1]
c.i.

The current drug.

[1]
c.ii.

State an assumption that the company is making, in order to use a t-test.

[1]
d.

State the hypotheses for this t-test.

[1]
e.

Find the p-value for this t-test.

[3]
f.

State the conclusion of this test, in context, giving a reason.

[2]
g.

Markscheme

stratified sampling        A1

[1 mark]

a.

0.2 × 18 = 3.6        M1A1

so 4 volunteers need to be chosen       A1

[3 marks]

b.

34.8 mg/dL      A1

[1 mark]

c.i.

24.7 mg/dL      A1

[1 mark]

c.ii.

EITHER

The decreases in cholesterol are distributed normally    A1

OR

The variance of the two groups of volunteers is equal.    A1

[1 mark]

d.

H 0 : N ¯ = C ¯ and  H 1 : N ¯ > C ¯          A1

where N and C represent the decreases of the new and current drug

[1 mark]

e.

df = 16, t = 2.77        (M1)

p-value = 0.00683        A2

[3 marks]

f.

Since 0.00683 < 0.01        R1

Reject H0. There is evidence, at the 1% level, that the new drug is more effective.       A1

[2 marks]

g.

Examiners report

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

Syllabus sections

Topic 4—Statistics and probability » SL 4.1—Concepts, reliability and sampling techniques
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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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