Portfolio task

Task 1:

A)

n = 450       (mean value) =87     s(standard deviation )= 7.50      adj s =7.508347248 [pic 1]

z critical= 2.575

 s x   =   7.50 x   = 7.508347248[pic 2][pic 3]

x 87 2.575 x  = 870.9114132254[pic 4][pic 5][pic 6][pic 7][pic 8]

Interpretation: At 99 % of confidence true mean value of cost is likely to be between 86.08858677 £ and 87.9114132254 £. In order to set up interval mean needs to be test by the result of z critical value multiply by adjusted standard deviation divide by square of total of items. As the items standard deviations is unknown sample standard deviation is adjusted. The z critical value is known from table and correspondent at 99% of confidence.

b) n = 450       (mean value) =2.3     s(standard deviation )= 0.38     adj s =0.3804229272[pic 9]

z critical= 2.575

 s x       =     0.38 x  = 0.3804229272                    [pic 10][pic 11]

x 2.3  2.575 x  = 2.3 0.04617827008[pic 12][pic 13][pic 14][pic 15][pic 16]

Interpretation: At 99 % of confidence true mean value of length of time in stock (in weeks) is likely to be between 2.25382173 and 2.3461782708. In order to set up interval mean needs to be test by the result of z critical value multiply by adjusted standard deviation divide by square of total of items. As the items standard deviations is unknown sample standard deviation is adjusted. The z critical value is known from table and correspondent at 99% of confidence.

c)  n=450    x=35     Proportion of slow moving stock P 35/450=0.07

P  z x  = 0.072.575 x  = 0.07 0.03097144518[pic 17][pic 18][pic 19][pic 20][pic 21]

Interpretation: We can be confident at 99% that the proportion of slow moving stock is between 3.902855482% and 10.09714452%.

Task 2:

A)

                                             Current sample n 1                             previous sample n 2

N                                               450                                                            300

Sample mean                        8.7                                        102

Sample s                        7.50                                12

Adjusted sample s                   7.508347248                        13.73485669

H 0:  µ current - µ previous  There is no difference between the costs stocked items[pic 22]

H 1: µ current - µ previous  There is a difference between the costs of stocked items[pic 23]

a= 0.05     z critical = -1.645 (one tailed test)

 Standard deviation adjusted calculation:

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