User interface language: English | Español

Date November 2018 Marks available 3 Reference code 18N.3.AHL.TZ0.Hsp_2
Level Additional Higher Level Paper Paper 3 Time zone Time zone 0
Command term Explain Question number Hsp_2 Adapted from N/A

Question

The times t , in minutes, taken by a random sample of 75 workers of a company to travel to work can be summarized as follows

t = 2165 t 2 = 76475 .

Let T be the random variable that represents the time taken to travel to work by a worker of this company.

Find unbiased estimates of the mean of T .

[1]
a.i.

Find unbiased estimates of the variance of T .

[2]
a.ii.

Assuming that T is normally distributed, find

(i)  the 90% confidence interval for the mean time taken to travel to work by the workers of this company,

(ii)  the 95% confidence interval for the mean time taken to travel to work by the workers of this company.

[3]
b.

Before seeing these results the managing director believed that the mean time was 26 minutes.

Explain whether your answers to part (b) support her belief.

[3]
c.

Markscheme

t ¯ = i = 1 75 t i 75 = 28.886 = 28.9        A1

 

[1 mark]

a.i.

s n 1 2 = 75 74 ( i = 1 75 t i 2 75 t ¯ 2 ) = 188.9009 = 189       (M1)A1

Note: Accept all answers that round to 28.9 and 189.

Note: Award M0 if division by 75.

 

[2 marks]

a.ii.

attempting to find a confidence interval.     (M1)

(i)   90% interval: (26.2, 31.5)       A1

(ii)  95% interval: (25.7, 32.0)       A1

 

Note: Accept any values which round to within 0.1 of the correct value.

Note: Award M1A1A0 if only confidence limits are given in the form 28.9 ± 2.6.

 

[3 marks]

b.

26 lies within the 95% interval but not within the 90% interval        R1

Note: Award R1 for considering whether or not one or two of the intervals contain 26.

 

the belief is supported at the 5% level (accept 95%)        A1

the belief is not supported at the 10% level (accept 90%)        A1

Note: FT their intervals but award R1A1A0 if both intervals give the same conclusion.

 

[3 marks]

c.

Examiners report

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

Syllabus sections

Topic 4—Statistics and probability » AHL 4.16—Confidence intervals
Show 21 related questions
Topic 4—Statistics and probability

View options