60
Reliability of Measurements
4.265 x (3081)- x 8.275 x 1Q-"
(g)
(h)
0.9820 x 1.0035
6.327 x 10-' x 7.056 x IP'
7 x 9.0038 x IQ-"
6.022 x 10
2i x 27.00 x 10~3. Water analysts often report trace impurities in water as "parts per million''—
that is, parts by weight of impurity per million parts by weight of water. In an
analysis, 2.5 liters of a water sample are evaporated to a very small volume in
a platinum dish; the residue is treated with a sensitive reagent that develops a
red color, whose intensity is a measure of the amount of nickel present. The
amount of nickel present is found to be 0.41 mg. How many parts per million
of nickel were present in the original sample of water? (Assume that the
density of water is 1 g/ml.)
4. State the precision, both in parts per thousand and in percentage, with which
each of the following measurements is made.
(a) 578 with a standard deviation of 2.0
(b) 0.0578 with a standard deviation of 0.00020
(c) 5078 with a standard deviation of 2.0
(d) 0.005078 with a standard deviation of 0.000030
(e) 0.0050780 with a standard deviation of 0.00000010
(f) 5078 with a standard deviation of 50
(g) 5.78 x 10' with a standard deviation of 2.0 x 10'
5. A radioactive sample shows the following counts for one-minute intervals:
2642; 2650; 2649; 2641; 2641; 2637; 2651; 2636. Find the average deviation, the
standard deviation, and the 90% confidence interval for a single value and for
the mean.
6. A student wishes to calibrate a pipet by weighing the water it delivers. A
succession of such measurements gives the following weights: 5.013 g; 5.023
g; 5.017 g; 5.019 g; 5.010 g; 5.018 g; 5.021 g. Calculate the average deviation
and the 95% confidence interval for a single value.
7. In determining the viscosity of a liquid by measuring the time required for 5.00
ml of the liquid to pass through a capillary, a student records the following
periods: 3 min 35.2 sec; 3 min 34.8 sec; 3 min 35.5 sec; 3 min 35.6 sec; 3 min
34.9 sec; 3 mm 35.3 sec; 3 min 35.2 sec. Find the average deviation and the
70% confidence interval for a single value, expressing both as a percentage.
8. A student wishes to determine the mole weight of a gas by measuring the time
required for a given amount of the gas to escape through a pinhole. He observes the following time intervals: 97.2 sec; 96.6 sec; 96.5 sec: 97.4 sec; 97.6
sec; 97.1 sec; 96.9 sec; 96.4 sec; 97.3 sec; 97.0 sec. Find the average deviation
and the 99% confidence interval for the mean, expressing both in parts per
thousand.
9. The height (h) to which a liquid will rise in a capillary tube is determined by
the force of gravity (g), the radius (/-) of the tube, and the surface tension (y)
and density (d) of the liquid at the temperature of the experiment. The relationship is y = \hdgr. A student decides to determine the radius of a capillary
Reliability of Measurements
4.265 x (3081)- x 8.275 x 1Q-"
(g)
(h)
0.9820 x 1.0035
6.327 x 10-' x 7.056 x IP'
7 x 9.0038 x IQ-"
6.022 x 10
2i x 27.00 x 10~3. Water analysts often report trace impurities in water as "parts per million''—
that is, parts by weight of impurity per million parts by weight of water. In an
analysis, 2.5 liters of a water sample are evaporated to a very small volume in
a platinum dish; the residue is treated with a sensitive reagent that develops a
red color, whose intensity is a measure of the amount of nickel present. The
amount of nickel present is found to be 0.41 mg. How many parts per million
of nickel were present in the original sample of water? (Assume that the
density of water is 1 g/ml.)
4. State the precision, both in parts per thousand and in percentage, with which
each of the following measurements is made.
(a) 578 with a standard deviation of 2.0
(b) 0.0578 with a standard deviation of 0.00020
(c) 5078 with a standard deviation of 2.0
(d) 0.005078 with a standard deviation of 0.000030
(e) 0.0050780 with a standard deviation of 0.00000010
(f) 5078 with a standard deviation of 50
(g) 5.78 x 10' with a standard deviation of 2.0 x 10'
5. A radioactive sample shows the following counts for one-minute intervals:
2642; 2650; 2649; 2641; 2641; 2637; 2651; 2636. Find the average deviation, the
standard deviation, and the 90% confidence interval for a single value and for
the mean.
6. A student wishes to calibrate a pipet by weighing the water it delivers. A
succession of such measurements gives the following weights: 5.013 g; 5.023
g; 5.017 g; 5.019 g; 5.010 g; 5.018 g; 5.021 g. Calculate the average deviation
and the 95% confidence interval for a single value.
7. In determining the viscosity of a liquid by measuring the time required for 5.00
ml of the liquid to pass through a capillary, a student records the following
periods: 3 min 35.2 sec; 3 min 34.8 sec; 3 min 35.5 sec; 3 min 35.6 sec; 3 min
34.9 sec; 3 mm 35.3 sec; 3 min 35.2 sec. Find the average deviation and the
70% confidence interval for a single value, expressing both as a percentage.
8. A student wishes to determine the mole weight of a gas by measuring the time
required for a given amount of the gas to escape through a pinhole. He observes the following time intervals: 97.2 sec; 96.6 sec; 96.5 sec: 97.4 sec; 97.6
sec; 97.1 sec; 96.9 sec; 96.4 sec; 97.3 sec; 97.0 sec. Find the average deviation
and the 99% confidence interval for the mean, expressing both in parts per
thousand.
9. The height (h) to which a liquid will rise in a capillary tube is determined by
the force of gravity (g), the radius (/-) of the tube, and the surface tension (y)
and density (d) of the liquid at the temperature of the experiment. The relationship is y = \hdgr. A student decides to determine the radius of a capillary