商品说明书：级别2商业统计（VRQ）ASE20096卷

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• Use
black ink or ball-point pen – pencil can only be used for graphs, charts, diagrams, etc.
• Fill in the boxes
at the top of this page with your name, candidate number, centre code and your candidate ID number.
• Answer
all questions.• Answer the questions in the spaces provided – there may be more space than you need.
• Answers should be given to an appropriate degree of accuracy.
Information
• The total mark for this paper is 100.
• The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.• A formulae sheet is provided at the front of this question paper.• Calculators may be used.
Advice
• Read each question carefully before you start to answer it.• Try to answer every question.
• You are advised to show your workings.
• Check your answers if you have time at the end.
Certificate in Business Statistics (VRQ)
Level 2
ASE20096
Monday 20 November 2017Time: 2 hours 30 minutes
Complete the details below in block capitals.
Candidate name
Centre Code Candidate Number
Candidate ID Number
Total Marks
P54282A
©2017 Pearson Education Ltd.
1/1/1/1/1/1
Paper Reference
Pearson LCCI
You must have:HB pencil, eraser
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4Answer ALL questions. Write your answers in the spaces provided.
1 AMG, a market gardening company, wishes to investigate the relationship between
the total weight of tomatoes produced by a tomato plant (y kilograms) and the
amount of fertiliser used (x grams).
An experiment was conducted by applying known amounts of fertiliser to similar
plants and weighing the resulting yields.
Here are the results obtained from 10 tomato plants.
Weight of fertiliser (x grams)Yield of tomatoes (y kilograms)
0 4.01
2 4.70
4 5.02
6 4.84
8 5.38
10 5.61
12 5.47
14 5.80
16 5.90
18 5.95
(a) State which of the two variables is the response variable.
You must give a reason for your answer.
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(b) Plot these data on a scatter diagram on the grid below.
(3)
The managing director of AMG says ‘The scatter diagram shows positive correlation’.
(c) Explain, in the context of the question, what this means.
(1)
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6When the data in the table are entered into a computer spreadsheet the following summary statistics are obtained.
∑ x= 90 ∑ y= 52.68 ∑ xy= 506 ∑ x2 = 1140
(d) Calculate the equation of the least squares regression line for yield of tomatoes
on weight of fertiliser.
(6)
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(e) Explain what the intercept and the gradient of the least squares regression line
tell AMG.
(3)
Intercept .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... Gradient .................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................... ....................................................................................................................................................................................................................................................................................
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(f) Estimate, using your equation in part (d), the weight of fertiliser needed for a
tomato plant to produce a yield of 5.20 kg.
(3)
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The correlation coefficient between weight of fertiliser and yield is 0.94
(g) Discuss the reliability of your estimate in part (f).
(2)
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(Total for Question 1 = 20 marks)
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8
2 The table shows the bonuses paid (x , $000) to a sample of 100 employees of LCV plc,
an insurance company, in 2016
Bonus paid (x , $000)Number of employees Total bonus payments x 4 7 14 4 < x 8 12 72 8 < x 9 20 170 9 < x 10 26 247 10 < x 16 29 377
16 < x 24
6
120
(a) Calculate an estimate for the mean bonus.
(3)
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(b) Calculate an estimate for the standard deviation.
(4)
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(c) Give a reason why the standard deviation might be a better measure of spread to
use in this case rather than the quartile deviation.
(1)
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(d) Using your answers from parts (a) and (b), calculate the coefficient of variation for
these data.
(2)
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(e) Explain what your answer to part (d) measures.
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10 The table of bonuses paid from page 8 is shown again here.
Bonus paid (x, $000)Number of employees Total bonus payments
x 4 7 14
4 < x 8 12 72
8 < x 9 20 170
9 < x 10 26 247
10 < x 16 29 377
16 < x 24 6 120
(f) Use these data to construct a Lorenz curve.
(7)
(g) Describe what the diagram shows about the distribution of bonuses paid in 2016
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(Total for Question 2 = 20 marks)
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assurance manager has to test the batteries regularly to ensure that they satisfy
quality standards.
In a day, the factory produces 5000 batteries and each battery has a unique barcode.
The quality assurance manager intends to select a sample of 120 of these batteries.
(a) Give two reasons why the quality assurance manager would take a sample rather
than a census of the batteries produced in a day.
(2)
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(b) Suggest a suitable sampling frame for the quality assurance manager to use.
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The quality assurance manager chooses to use simple random sampling to select the
120 batteries.
(c) Describe how the quality assurance manager would do this.
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(e) Estimate the modal time from the histogram.
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(f) Estimate the percentage of these batteries that last less than 430 minutes.
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One of these batteries is selected at random.
(g) Calculate the probability that this battery lasted longer than 525 minutes.
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(Total for Question 3 = 20 marks)。