Quantitative Methods (Statistics)

Quantitative Methods

Time allowed - 2 hours Full marks will be given for complete answers to all questions in Section A and to two questions in Section B. In Section B credit will be given for the best two answers. Calculators are permitted, provided they are silent, self-powered, without communications facilities, and incapable of holding text or other material that could be used to give a candidate an unfair advantage. They must be made available on request for inspection by invigilators, who are authorised to remove any suspect calculators. Statistical Tables are provided.

FORMULAE

The following results or formulae may be quoted and used in any question, provided you make clear that you are doing so. Binomial Distribution P (R = r) = n Cr pr (1 p)n r for r = 0; 1; 2; :::; n; where

n

n! ; and n! = n(n r!(n r)! ER = np and Var R = np(1 p): Cr =

1)(n

2):::3:2:1

Poisson Distribution P (N = n) = e

t

( t)n ; for n = 0; 1; 2; ::: n!

EN = t = Var N:

c 2 0 0 7 U n ive rsity o f Wa le s A b e ry stw y th

2/7/2007

MBM6010:) Quantitative Methods (Statistics) Section A All questions carry 5 marks

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1. Twelve strips of cotton are dyed and subjected to a fading test. After the test, the strength of colour is measured as follows: 7:4 8:3 8:1 7:3 8:2 8:5 7:7 6:2 8:3 6:1 6:9 7:5 Calculate the sample mean of this data and its estimated standard error. 2. The manager of a chemist’ shop has recorded the number of bottles sold in one s month for 16 di¤erent varieties of Eau-de-Cologne. Appendix Q2 gives some Minitab output from the Fitted Line Plot routine where the number of bottles sold is the Y variable and the price (£ ) per bottle is the X variable. (a) What change in sales would you expect if the price of one variety is decreased by £ 7.50 per bottle? (b) How many bottles of an Eau-de-Cologne priced at £ 40 per bottle would you predict will be sold in one month? 3. In a survey of 400 customers at a supermarket, 250 said they...