User interface language: English | Español

Date November 2017 Marks available 2 Reference code 17N.3.AHL.TZ0.Hsp_2
Level Additional Higher Level Paper Paper 3 Time zone Time zone 0
Command term Interpret and Justify Question number Hsp_2 Adapted from N/A

Question

Anne is a farmer who grows and sells pumpkins. Interested in the weights of pumpkins produced, she records the weights of eight pumpkins and obtains the following results in kilograms.

7.7 7.5 8.4 8.8 7.3 9.0 7.8 7.6

Assume that these weights form a random sample from a N ( μ ,   σ 2 ) distribution. 

 

Anne claims that the mean pumpkin weight is 7.5 kilograms. In order to test this claim, she sets up the null hypothesis H 0 : μ = 7.5 .

Determine unbiased estimates for μ and σ 2 .

[3]
a.

Use a two-tailed test to determine the p -value for the above results.

[3]
b.i.

Interpret your p -value at the 5% level of significance, justifying your conclusion.

[2]
b.ii.

Markscheme

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

UE of μ is 8.01   ( = 8.0125 )     A1

UE of σ 2 is 0.404     (M1)A1

 

Note:     Accept answers that round correctly to 2 sf.

 

Note:      Condone incorrect notation, ie, μ instead of UE of μ and σ 2 instead of UE of σ 2 .

 

Note:     M0 for squaring 0.594 giving 0.354, M1A0 for failing to square 0.635

 

[3 marks]

a.

attempting to use the t -test     (M1)

p -value is 0.0566     A2

 

Note:     Accept any answer that rounds correctly to 2 sf.

 

[3 marks]

b.i.

0.0566 > 0.05     R1

we accept the null hypothesis (mean pumpkin weight is 7.5 kg)     A1

 

Note:     Apply follow through on the candidate’s p -value.

 

Note:     Do not award A1 if R1 is not awarded.

 

[2 marks]

b.ii.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.

Syllabus sections

Topic 4—Statistics and probability » AHL 4.18—T and Z test, type I and II errors
Show 102 related questions
Topic 4—Statistics and probability

View options