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ChE 311.3 – Mathematical Modelling I
Assignment # 4
October 30th
November 6th (beginning of class)
Posted:
Due:
The following questions are taken from “Statistics and Probability for Engineering
Applications” by W. J. DeCoursey.
1.
Benzene in the air workers breathe can cause cancer. It is very
important for the benzene content of air in a particular plant to be not more
than 1.00 ppm. Samples are taken to check the benzene content of the air. 25
specimens of air from one location in the plant gave a mean content of 0.760
ppm, and the standard deviation of benzene content was estimated on the
basis of the sample to be 0.45 ppm. Benzene contents in this case are found
to be normally distributed.
a)
Is there evidence at the 1% level of significance that the true mean
benzene content is less than or equal to 1.00 ppm?
b)
Find the 95% confidence interval for the true mean benzene content.
2.
The mean height of 61 males from the same state was 68.2 inches
with an estimated standard deviation of 2.5 inches, while 61 males from
another state had a mean height of 67.5 inches with an estimated standard
deviation of 2.8 inches. The heights are normally distributed. Test the
hypothesis that males from the first state are taller than males from the
second state.
a)
b)
Use a level of significance of 5%.
Use a level of significance of 10%.
3.
On last year’s final examination in statistics, the marks of two
different sections had the numbers, means and standard deviations shown in
the table below:
n
41
51
x
sx
64.3
59.5
15.6
17.2
The marks were normally distributed.
a)
b)
Were the means in the two sections significantly different? Use the
5% level of significance.
The overall average of all the students in the last 10 years of
statistics final examinations was 61.7 with a standard deviation of
16.8. Was the section average for the 41 students shown above
significantly higher than the overall average? Use the 5% level of
significance.
4.
Two flow meters, A and B, are used to measure the flow rate of brine
in a potash processing plant. The two meters are identical in design and
calibration and are mounted on two adjacent pipes, A on pipe 1 and B on
pipe 2. On a certain day, the following flow rates (in m3/sec) were observed
at 10-minute intervals from 1:00 pm to 2:00 pm.
1:00 pm
1:10 pm
1:20 pm
1:30 pm
1:40 pm
1:50 pm
2:00 pm
Meter A
1.7
1.6
1.5
1.4
1.5
1.6
1.7
Meter B
2.0
1.8
1.6
1.3
1.6
1.7
1.9
Is the flow in pipe 2 significantly different from the flow in pipe 1 at the 5%
level of significance?
5.
A testing laboratory is trying to make its results more consistent by
standardizing certain procedures. From a sample of size 28 the sample
standard deviation by the revised procedure is found to be 1.74 units.
Plotting concentrations on normal probability paper did not show any
marked departure from a normal distribution. Is there evidence at the 5%
level of significance that the sample standard deviation is significantly less
that the former population standard deviation of 2.92 units?