BCSL-044
1. The
volume of milk contained in one liter packets (in liters) is given below.
Perform the tasks given in (i) to (iv) using a spreadsheet package:
|
1.004
|
0.994
|
1.076
|
1.063
|
0.964
|
1.171
|
0.995
|
1.076
|
1.011
|
1.111
|
|
|
1.000
|
0.968
|
1.056
|
0.999
|
1.001
|
0.959
|
1.001
|
0.977
|
1.101
|
0.959
|
|
|
0.984
|
1.036
|
1.013
|
0.984
|
1.161
|
0.975
|
0.980
|
1.013
|
1.001
|
1.010
|
|
|
0.977
|
1.045
|
0.993
|
1.058
|
0.991
|
1.091
|
0.925
|
1.054
|
1.034
|
0.949
|
|
|
1.023
|
1.012
|
0.934
|
1.066
|
0.979
|
0.986
|
1.013
|
1.014
|
1.000
|
1.024
|
|
(i) Find the minimum and maximum volume using
spreadsheet formula.
(ii) Create 5
classes with suitable class interval and create the frequency distribution for
volume using Array formula.
(iii) Find the percentage of packets having volume
less than a liter.
(iv) Represent the frequency distribution with the
help of a relevant graph.
2. Perform
the following tasks using a spreadsheet (you must either enter necessary
formula that are required to calculate the value or you may use spreadsheet
function for the same):
(i) Given a
population of 5000 and a sample size of 20 with a standard deviation of 10;
calculate the standard error.
(ii) A company
manufactures nails of different lengths. The nails with length 2 inch should
have a mean diameter of 3 mm. A sample of 100 nails was taken out of a lot
consisting of 10000 such nails. The mean sample diameter was found to be 3.01
mm having a standard deviation of 0.03 mm. Assuming a confidence level of 95%,
will you accept the nail lot. Justify your answer. Make suitable assumption, if
any.
3. Measure
control department checked the 5 kg weights of four different manufacturers.
Four samples of each of these manufacturers were tested. The findings are given
in the following table:
Data on Five kg Weights
|
Sample
|
Manufacturer
|
||||
|
A
|
B
|
C
|
D
|
||
|
1
|
5.05
|
5.02
|
5.21
|
4.88
|
|
|
2
|
4.99
|
4.97
|
5.15
|
5.01
|
|
|
3
|
5.01
|
4.89
|
5.09
|
4.89
|
|
|
4
|
5.03
|
4.87
|
4.93
|
5.00
|
|
Perform an ANOVA using any software to test (at 5%
level) whether all the four manufacturers are producing proper weights. Make
suitable assumptions, if any.
4. A Petrol filling
station records the details of sales of petrol every day. The following table
shows the sale of petrol by the company. Use spreadsheet software to find the
moving averages for the length of 4 and 5.
|
Day
|
Sale (Liters per day)
|
|
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
|
9507
8013
7000
6565
9989
4333
3000
2066
5505
3243
5067
4546
4333
6899
5459
|
5. A company
manufactures pipes of 1 meter diameter. The company takes five observations of
the diameter of the pipe on each day. These observations are taken 5 times
during a working day. Calculate the control limits for mean and range, and plot
the control charts using any statistical software. Make suitable assumptions,
if any. The data is given in the following table:
|
Sample Days
|
The diameter of the pipe (meters)
|
||||
|
1
2
3
4
5
|
1.003
0.990
1.033
1.103
0.973
|
1.007
0.997
1.035
1.001
1.045
|
1.010
1.050
1.000
1.000
1.025
|
1.009
1.049
0.929
0.979
1.022
|
0.995
1.055
0.915
0.955
0.999
|
(Please
take the suitable values of d2, d3, d4, A2
and other variables.)
6. A
stationery selling company sells stationery items as per the following table.
Fit a trend using any statistical software to sales data for this company. Make
suitable assumptions.
|
Month
|
Mar
|
Apr
|
May
|
June
|
Jul
|
Aug
|
Sept
|
|
Sales (Units)
|
2000
|
8000
|
4000
|
1000
|
3000
|
3000
|
4000
|
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