Q1 The Sales Director of a retail chain store is developing the future strategy of the
firm. She carries out a study on the Annual Sales per square metre of floor space in
a number of stores in two different areas within the same city, and the results are
shown below:
。 7
，：
(a) Is there any evidence that the Sales per Square Metre is different between the
two different areas?
？
(b) Does the data support the belief that the level of sales is directly dependent
on the area of floor space?
：，
(c) If so, plot the graph and find the relationship and the 95% confidence
interval for the slope.
， plot ，
excel ，， 95%
for the slope（）
(d) If a new store with 250 square metres of floor space were to be opened in
Area 1 what level of annual sales would be expected?
250 1，
？
(e) Find the 95% confidence interval for the prediction in (d), above.
d 95%
(f) Does the data suggest that the plotted line should pass through the origin?
plotted ？
Q2. (i) An Internet Service Provider (ISP) claims that if any loss of service occurs
before mid-day it will restore the service on the same day. Past data indicates that
the probability of all repairs being completed on the same day is actually 0.7.
For the first FIVE problems reported on a given day, what is the probability that:
(a) All five will be repaired on the same day?
(b) At least three will be repaired on the same day?
(c) Fewer than two will be repaired on the same day?
(d) What are the mean and standard deviation of the probability distribution in (a)?
(ii) Two analysts carry out simultaneous tests on the amount of contaminant in the
output from a chemical process to find the extent of any bias between their methods.
The results (in ppm) are shown in the table below:
(a) Does the data suggest that there is any difference between the operators’
methods?
(b) If so, what are the 95% confidence limits of the difference?
Q3. (i) A soft drinks producer wishes to have consistent “fill” levels in the bottles
exiting its bottling process. In fact, there is some deviation from target and they
want to determine if this is caused by the line speed (i.e. the number of bottles filled
per minute). Accordingly, they carry out an experiment in which four different line
speeds are applied at each of two levels of carbonation, and the results are shown
below (the figures show the deviation from the target fill level).
(a) Does the data suggest that line speed does influence fill level?
(b) Is there any interaction between carbonation and line speed?
(ii) A packaging firm finds that the number of breakdowns on its automated
production line averages 1.5 per eight hour shift. This is constant for all three shifts.
(a) Suggest a model that is likely to be appropriate for modelling this data.
(b) What is the probability of exactly two breakdowns during the night shift?
(c) What is the probability of less than two breakdowns during the afternoon shift?
(d) What is the probability of no breakdowns during three consecutive shifts?
Q4. (i) It has been suggested that the use of Railways and Waterways for the internal
transportation of goods in Europe is in decline. The data below shows the percentage
of goods moved by Railways and Waterways within a country for the years 2000 and
2009.
Do the data support the suggestion?
(ii) The air in a “clean room” used for the production of electronic devices is cleaned
by filtering. The air on the outside of the filters is monitored daily to check that
ambient conditions are not changing significantly. The table below shows the results
of counting the number of dust particles in a standard volume of air over a period of
time:
(a) Suggest a model that is likely to be appropriate for modelling this data and verify
your choice.
(b) If a sample taken at a later date has 7 particles in a standard sample, does it seem
that air quality is deteriorating? (Explain your answer, and choice of test.)
Q5. (i)A logistics company in Hong Kong has monitored the performance of their
parcel-sorting machinery. The planned Availability (Ai) requires a maximum allowable Time
to Repair (TTR) of one and a half hours. They have recorded the TTR when the machinery
breaks down, and the results are summarised below:
(a) What distribution would seem most appropriate to model the TTR data? (Provide clear
evidence for your conclusion).
(b) If your suggested model were valid what proportion of TTR values is likely to exceed the
maximum allowable?
(c) Their calculation of Ai requires the Mean Time to Repair (MTTR). Within what limits
can the MTTR be quoted with 95% confidence?
(ii) The Singapore branch of the same firm uses a different version of the parcel-sorting
machinery. A pilot study on the TTR for this machine gave the following results:
(e) Is the TTR in Hong Kong significantly better than in Singapore?
(ii) A company wishes to compare the effectiveness of Computer Assisted Learning
with conventional Group-Based Learning as a means of training its staff. Two
groups of employees are assigned, at random, to the different methods and their
performance is then assessed by timing how long they take to assemble one of the
firm’s products. The results, in seconds, are shown in the table below:
Does the data indicate any significant difference between the two methods?