Practise questions · Salam Academy

SA-9709-P6-HT2-0013 marksL1 FoundationCalculatorTests for a mean

A population has standard deviation

10

. A random sample of

25

has mean

104

. Test

H_0:\mu=100

against

H_1:\mu>100

at the

5\%

level. Give the test statistic and your decision.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT2-0061 markL1 FoundationCalculatorTests for a mean

In a two-tailed test at the

5\%

level, the test statistic is

z=1.8

. The correct decision is

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT2-0071 markL1 FoundationCalculatorLarge-sample tests

A test for a mean uses a sample of

80

from a population whose distribution is unknown. Why can the normal distribution still be used?

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT-Q011 markL1 FoundationCalculatorTests for a mean

For a two-tailed test at the

5\%

level using the normal distribution, the critical values are

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT-0034 marksL2 StandardCalculatorTests for a mean

A population has standard deviation

5

. A random sample of

36

has mean

51.8

. Test

H_0:\mu=50

against

H_1:\mu\ne50

at the

5\%

level. Give the test statistic and conclusion.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT2-0023 marksL2 StandardCalculatorTests for a mean

A population has standard deviation

8

. A random sample of

64

has mean

52.2

. Test

H_0:\mu=50

against

H_1:\mu\ne50

at the

1\%

level. Give the test statistic and your decision.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT2-0033 marksL2 StandardCalculatorLarge-sample tests

A random sample of

100

from a population of unknown distribution has mean

48.6

, and an unbiased estimate of the variance is

36

. Test

H_0:\mu=50

against

H_1:\mu<50

at the

5\%

level. Give the test statistic (3 s.f.) and your decision.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT2-0042 marksL2 StandardCalculatorTests for a mean

A population has standard deviation

12

. A test of

H_0:\mu=80

against

H_1:\mu>80

uses a sample of

36

at the

5\%

level. Find the critical value of

\bar x

, correct to 2 decimal places.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT-0044 marksL3 ExamCalculatorTests for a mean

A machine fills bags with mean

200

g and standard deviation

12

g. After servicing, a sample of

16

bags has mean

205

g. Test at the

5\%

level whether the mean has increased.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT-0103 marksL3 ExamCalculatorTests for a mean

X

has standard deviation

4

. A test of

H_0:\mu=30

against

H_1:\mu<30

uses a sample of

25

at the

1\%

level. Find the critical value of

\bar x

, correct to 2 decimal places.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT2-0083 marksL3 ExamCalculatorTests for a mean

A population has standard deviation

15

. A test of

H_0:\mu=200

against

H_1:\mu<200

uses a sample of

25

at the

1\%

level. Find the largest value of

\bar x

that leads to rejecting

H_0

, correct to 2 decimal places.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P6-HT2-0056 marksL4 ChallengingCalculatorLarge-sample tests

A random sample of

50

values gives

\Sigma x=2580

and

\Sigma x^2=134\,500

. Test at the

5\%

level whether the population mean is greater than

50

. Give the unbiased variance estimate, the test statistic (3 s.f.) and your decision.

Salam Academy Original Practice · Proposed mark scheme

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