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(Solved) Assignment 3 Exercise 1 (10 marks) One step in the manufacture of a certain metal clamp involves the drilling of four holes. In a sample of 150


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Assignment 3
Exercise 1 (10 marks)
One step in the manufacture of a certain metal clamp involves the
drilling of four holes. In a sample of 150 clamps, the average time
needed to complete this step was 72 seconds and the standard
deviation was 10 seconds.
(a)
Find an 87% confidence interval for the mean time needed to
complete the step.
(b)
What is the confidence level of the interval (69, 75)?
(c)
How many clamps must be sampled so that the width of a
93.5% confidence interval is 3?
(d)
Find a 96% upper confidence bound for the mean time to
complete the step.
Exercise 2 (12 marks)
As part of the quality-control program for a catalyst manufacturing line,
the raw materials (alumina and a binder) are tested for purity. The
process requires that the purity of the alumina is to be 85%. A random
sample from a recent shipment of alumina yielded the following results
(in %):
93.2
87.0
92.1
90.1
87.3
93.6
a) Test the requirements of the catalyst manufacturing line using the
appropriate hypothesis test (assume 0.05 ).
b) Verify your result in part (a) using the appropriate confidence
interval.
Exercise 3 (14 marks)
Fifty specimens of a new computer chip were tested for speed in a
certain application, along with 50 specimens of chips with the old
design. The average speed, in MHz, for the new chips was 495.6, and
the standard deviation was 19.4. The average speed for the old chips
was 481.2, and the standard deviation was 14.3.
a) Can you conclude a significant difference in the mean speed
between the new and old chips?
b) Verify your result in part a) using the appropriate confidence
interval.
c) A sample of 60 even older chips had an average speed of 391.2
MHz with a standard deviation of 17.2 MHz. Someone claims
that the new chips average more than 100 MHz faster than these
very old ones. Do the data provide convincing evidence for this
claim?
Exercise 4 (16 marks) Two methods for measuring the molar heat of fusion of water are being
compared. Ten measurements made by method A have a mean of
6.02 kilojoules per mole (kJ/mol) with a standard deviation of 0.02
(kJ/mol). Five measurements made by method B have a mean of 6.00
kJ/mol and a standard deviation of 0.01 kJ/mol.
a) Can you conclude that the mean measurements for method A is
greater than that of method B?
b) Repeat this test based on the knowledge that the population
variances were equal.
c) Find an 80% two sided confidence interval based on the
knowledge of “equal variances”.
Exercise 5 (12 marks)
Two microprocessors are compared on a sample of six benchmark
codes to determine whether there is a difference in speed. The times
(in seconds) used by each processor on each code are given in the
following table.
Code
1
2
3
4
5
6
Processor A 27.2
18.1
27.2
19.7
24.5
22.1
Processor B
24.1
19.3
26.8
20.1
27.6
29.8
a) Can you conclude that the mean speeds of the two processors
differ?
b) Verify your result in part a) using the appropriate confidence
interval. DUE DATE: THURSDAY, MARCH 23RD BY 3PM IN ANY
DROP BOX LABELLED “PAULA DICATO STAT2800”
LOCATED ON THE 4TH FLOOR OF THE UA BUILDING.
ASSIGNMENTS ARE DONE INDIVIDUALLY. LATE
ASSIGNMENTS ARE NOT ACCEPTED. THIS ASSIGNMENT
IS TO BE COMPLETED ENTIRELY BY HAND.

 


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