Edexcel IAL Mathematics S3.3.8 large-sample results
Practise large-sample inference by forming z tests for one or two means, then linking the decision to a contextual recommendation.
- Syllabus
- First assessment 2019
- Course
- Mathematics YMA01
- Level
- A2
Practise large-sample inference by forming z tests for one or two means, then linking the decision to a contextual recommendation.
A greengrocer is investigating the weights of two types of orange, type A and type B. She believes that on average type A oranges weigh greater than 5 grams more than type B oranges. She collects a random sample of 40 type A oranges and 32 type B oranges and records the weight, x grams, of each orange.
The table shows a summary of her data.

Test, at the 5% level of significance, the greengrocer's belief. You should state the hypotheses and the critical value used for this test.
H0:μA−μB=5
B1
H1:μA−μB>5
B1
s.e. =4045.4256…+3226.4232… (=awrt 1.4)
M1
z= s.e. ±(140.4−134.7−5)= awrt 0.50
dM1 A1
c.v. =1.6449
B1
(Do not reject H0 ) Insufficient evidence to support the greengrocer's belief.
(Insufficient evidence that the difference in weight between type A oranges and
type B oranges is over 5 grams).
A1ft
(7)
Explain how you have used the fact that the sample sizes are large in your answer to part (b).
Large sample sizes so...
Sample means are normally distributed (CLT)
B1
sA2=σA2 and sB2=σB2
B1
(2)
Total 12
Notes
(a)
M1 one correct expression
A1 either awrt 45.4 or awrt 26.4
A1 both awrt 45.4 and awrt 26.4
(b)
B1 Allow equivalent rearrangements. Must use μ
B1 Allow equivalent rearrangements. Must use μ.
For both hypotheses do not allow e.g. μ1 and μ2 unless each has been clearly defined
M1 attempt at standard error (allow one slip) ft their (a)
dM1 standardising with (140.4-134.7 - 5) and their s.e. (dep on previous M1)
A1 for 0.5 or awrt 0.50
B1 correct c.v. 1.6449 or better. Allow -1.6449 or better with use of μB−μA
Allow p= awrt 0.309
A1ft correct ft conclusion in context with either greengrocer's belief (oe) or difference in weights (oe) dependent on all B and M marks scored.
(c)
B1 must comment on both sample means, Aˉ and Bˉ
B1 must comment on both variances/standard deviations
Question
Number
Scheme
Marks