Practise questions · Salam Academy

SA-9709-P6-HT1-0014 marksL1 FoundationCalculatorBinomial tests

A coin shows

9

heads in

10

throws. Test at the

5\%

significance level whether the coin is biased towards heads. Give

P(X\ge9)

under

H_0

(3 s.f.) and your conclusion.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT1-0061 markL1 FoundationCalculatorBinomial tests

A manufacturer claims

10\%

of its products are faulty. A consumer group believes the proportion has changed. The alternative hypothesis is

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT-Q021 markL1 FoundationCalculatorBinomial tests

The null hypothesis

H_0

usually states that

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT-0014 marksL2 StandardCalculatorBinomial tests

A coin is suspected of being biased towards heads. In

12

throws it shows

10

heads. Test at the

5\%

level. Give

P(X\ge10)

under

H_0

(3 s.f.) and your conclusion.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT-0024 marksL2 StandardCalculatorPoisson tests

Accidents at a junction occur at an average of

4

per day. After changes, there is

1

accident on a randomly chosen day. Test at the

5\%

level whether the rate has fallen. Give

P(X\le1)

(3 s.f.) and your conclusion.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT1-0023 marksL2 StandardCalculatorBinomial tests

X\sim B(25,p)

. A test of

H_0:p=0.2

against

H_1:p<0.2

is carried out at the

5\%

level. The critical region is

X\le c

. Find

c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT1-0034 marksL2 StandardCalculatorPoisson tests

A shop received an average of

6

complaints a week. After new staff training, a randomly chosen week has

2

complaints. Test at the

5\%

level whether the rate of complaints has fallen. Give

P(X\le2)

(3 s.f.) and your conclusion.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT1-0052 marksL2 StandardCalculatorPoisson tests

A test of

H_0:\lambda=5

against

H_1:\lambda>5

rejects

H_0

if

X\ge10

, where

X\sim\text{Po}(\lambda)

. Find the actual significance level of the test, correct to 3 significant figures.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT-G014 marksL2 StandardCalculatorBinomial tests

A treatment succeeds for

30\%

of patients. In a trial of a new method on

20

patients, only

2

succeed. Test at the

5\%

significance level whether the success rate is lower with the new method. Give the probability you compare (3 s.f.) and your conclusion.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT-0094 marksL3 ExamCalculatorPoisson tests

Emails arrive at

2.5

per hour on average. On a day after a website change,

17

arrive in

4

hours. Test at the

5\%

level whether the rate has increased. Give

P(X\ge17)

(3 s.f.) and your conclusion.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT1-0044 marksL3 ExamCalculatorBinomial tests

It is claimed that a coin is fair. In

20

throws it shows

15

heads. Test at the

5\%

level whether the coin is biased (in either direction). Give

P(X\ge15)

(3 s.f.) and your conclusion.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT-0084 marksL4 ChallengingCalculatorBinomial tests

X\sim B(20,p)

. A test of

H_0:p=0.4

against

H_1:p>0.4

is carried out at the

5\%

level. Find the critical region

X\ge c

, giving the value of

c

.

Salam Academy Original Practice · Proposed mark scheme

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