Q1 Intelligence test scores out of 100 for a large group of students have been collected on the worksheet entitled TEST
a)Construct a frequency table of the results, using a maximum of 10 groups, and enter your values in the table below.
(20 marks)
Lower ClassBoundary / Upper Class
Boundary / Frequency
(f)
0 / 9
b)What do you notice about the distribution of the data? How would you expect the mean and median values to relate to each other?
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(15 marks)
c)How many students took the intelligence test?
(5 marks)
d)The ‘pass’ mark for the intelligence test is 40%. How many students passed the test?
(5 marks)
e)What percentage of students failed the test?
(5 marks)
f) If 70% or over gives a ‘high intelligence’ result, how many students are regarded as of ‘high intelligence’?
(5 marks)
g) What percentage of students achieved a ‘high intelligence result?
(5 marks)
h)What is the mean result?
(5 marks)
i)What is the median result?
(5 marks)
j)What is the range of the data?
(5 marks)
k)What is the standard deviation of the data?
(5 marks)
l)It has been decided that the intelligence test had been marked too strictly so that all the results need to be raised by 4%. What percentage now failed the test by scoring less than 40%?
(10 marks)
m)A new set of students now takes the intelligence test. The mean mark is 60% and the standard deviation is 30. Find the co-efficient of variation for both the original and the new set of students. What do you conclude?
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(10 marks)
2A firm is trying to decide between two projects. The expected annual profits at year end have been entered on the worksheet entitled NPV. If the discount rate is 8.25% answer the following questions:
a)What are the discount factors for the following years:
(10 marks)
b)What is the NPV?
(15 marks)
c)What is the average rate of return?
(15 marks)
d) What is the internal rate of return?
(15 marks)
e)On the basis of this analysis, how would you suggest your company should view the respective projects?
(25 marks)
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f)If the discount rate changed to 9% what are the discount factors (to 2 decimal places) for the following years:
(10 marks)
g)What is the NPV at the discount rate of 9%?
(10 marks)
Question 3
The data from the worksheet called CAPACITY gives the total number of visitors to a holiday destination in each of ten weeks and the number of coaches entering the central coach station each week. Although visitors can also arrive by train, by plane or by private car, the suggestion is that the total number of visitors to the holiday destination (Y) is linked to the weekly number of coaches (X) arriving at the destination.
a)What is the value of ?
(10 marks)
b)What is the value of ?
(10 marks)
b)c) Calculate the regression equation
i)i,
ii)∑xi2
iii)∑yi2
iv)∑i, xi2
(15 marks)
d)How many visitors would you expect from the regression equation if the number of coaches arriving each week is 20?
(10 marks)
c)Why is the regression equation sometimes called the ‘least squares line’?
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(10 marks)
f)A new coach station is to be built and up to 80 coaches can now arrive each week. If the maximum capacity of 80 coaches per week is reached, how many visitors might we predict?
(10 marks)
g) Does the coefficient for the independent variable have the sign you expected? Explain your reasoning.
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(10 marks)
h)Calculate the co-efficient of determination (R2)
(15 marks)
a)How confident can you be when you use the regression equation for forecasting the future number of visitors?
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(10 marks)
4
Answer both parts (i) and (ii) of this question
Part (i)
a)Identify the components involved in time series analysis.
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(5 marks)
b) Sales of boats over a 3-year period are entered on the worksheet entitled BOATS.
Find the centred moving average (to 2 decimal places) for the number of boats sold in the four quarters of year 2.
Q1 / Q2 / Q3 / Q4(20 marks)
c) What component of the time series have you found in part b)?
(5 marks)
d) Find the seasonal variation (S) for each quarter (to 2 decimal places)
(15 marks)
e) The answers in part d) are unadjusted seasonal variations (S) for each quarter. What is the adjustment factor you would apply to each?
(5 marks)
Part (ii)
A customer has complained that the weight of packets of tea is less than the stated 30 grams. A randomly chosen sample of packets of tea was selected by the authorities, with their weights entered on the worksheet entitled TEA.
. Test the hypothesis at the 5% level of significance that the packets of tea are consistently produced at a weight of 30 grams.
a) State your hypothesis
(10 marks)
b) State the critical value
(10 marks)
c) What is the value of the test statistic?
(20 marks)
d) What are your conclusions?
(10 marks)
Q5
There are 86 houses for sale of a similar size in each of two towns, Town A and Town B. The frequency distribution of the asking price (£000) of the houses in each town is shown on the worksheet called HOUSES
a)What is the mean house price in Town A?
(10 marks)
b)What is the median house price in Town A?
(10 marks)
c)What is the standard deviation of house prices in Town A?
(10 marks)
d)What is the mean house price in Town B?
(10 marks)
e)What is the median house price in Town B?
(10 marks)
f)What is the standard deviation of house prices in Town B?
(10 marks)
g)Briefly compare the distribution of house prices in Town A with the distribution of house prices in Town B. Identify and explain any differences between the two distributions.
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(20 marks)
h)Calculate the Co-efficient of Variation for house prices in each town
Town A
Town B
(10 marks)
i)What do your results in part h) above suggest?
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(10 marks)