62
Reliability of Measurements
(c) 6.82 with a standard deviation of 4.0 x 10~
:i
(d) 682 with a standard deviation of 4.0
(e) 0.00682 with a standard deviation of 0.0000040
(f) 6.82 x 10" with a standard deviation of 4000
(g) 0.0682 with a standard deviation of 0.004
16. A radioactive sample shows the following counts for one-minute intervals:
3262; 3257; 3255; 3265; 3257; 3264; 3259. Calculate the average deviation and
the 60% confidence interval for the mean.
17. A student wishes to calibrate a pipet by weighing the water it delivers. A
succession of such determinations gives the following weights in grams: 4.993;
4.999; 4.991; 4.994; 4.995; 4.995. Find the average deviation, the standard
deviation, and the 70% confidence interval for a single value.
18. If the viscosity of a given liquid is known, the viscosity of another may be
determined by comparing the time required for equal volumes of the two
liquids to pass through a capillary. To do this, a student makes the following
observations of time intervals: 4 min 9.6 sec; 4 min 8.8 sec; 4 min 10.2 sec; 4
min 9.8 sec; 4 min 9.0 sec. Find the average deviation and the 90% confidence
interval for the mean, expressing both in parts per thousand.
19. The time required for a given amount of gas to effuse through a pinhole under
prescribed conditions is a measure of its molecular weight. A student making
this determination observes the following effusion times: 1 min 37.3 sec; 1 min
38.5 sec; 1 min 36.9 sec; 1 min 37.2 sec; 1 min 36.5 sec; 1 min 38.7 sec; 1 min
37.0 sec. Find the average deviation and the 99% confidence interval for a
single value, expressing both as percentages.
20. The surface tension of a liquid may be determined by measuring the height to
which it will rise in a capillary of known radius. A student makes the following
observations of capillary rise with an unusual liquid that he has just prepared
in the laboratory: 63.2 mm; 63.5 mm; 62.9 mm; 62.8 mm; 63.7 mm; 63.4 mm.
Find the average deviation of these heights and the 90% confidence interval
for the mean, expressing both in parts per thousand.
21. How accurately should the values of liquid density and capillary radius be
known if all of the figures in the measurements in Problem 20 are to be
considered significant?
22. A graduated tube arranged to deliver variable volumes of a liquid is called a
buret. If a buret can be read to the nearest 0.01 ml, what total volume should
be withdrawn so that the volume will be known to a precision of 3 parts per
thousand? (Remember that two readings of the buret must be made for every
volume of liquid withdrawn.)
23. At some time or another, nearly everyone must decide whether to reject a
suspicious-looking result or to include it in the average of all the other results.
There is no agreement on what criteria should be used but, lacking information
about errors made in the experimental procedure, a rejection may be made on
the following statistical basis. If d and r are, respectively, the differences
Reliability of Measurements
(c) 6.82 with a standard deviation of 4.0 x 10~
:i
(d) 682 with a standard deviation of 4.0
(e) 0.00682 with a standard deviation of 0.0000040
(f) 6.82 x 10" with a standard deviation of 4000
(g) 0.0682 with a standard deviation of 0.004
16. A radioactive sample shows the following counts for one-minute intervals:
3262; 3257; 3255; 3265; 3257; 3264; 3259. Calculate the average deviation and
the 60% confidence interval for the mean.
17. A student wishes to calibrate a pipet by weighing the water it delivers. A
succession of such determinations gives the following weights in grams: 4.993;
4.999; 4.991; 4.994; 4.995; 4.995. Find the average deviation, the standard
deviation, and the 70% confidence interval for a single value.
18. If the viscosity of a given liquid is known, the viscosity of another may be
determined by comparing the time required for equal volumes of the two
liquids to pass through a capillary. To do this, a student makes the following
observations of time intervals: 4 min 9.6 sec; 4 min 8.8 sec; 4 min 10.2 sec; 4
min 9.8 sec; 4 min 9.0 sec. Find the average deviation and the 90% confidence
interval for the mean, expressing both in parts per thousand.
19. The time required for a given amount of gas to effuse through a pinhole under
prescribed conditions is a measure of its molecular weight. A student making
this determination observes the following effusion times: 1 min 37.3 sec; 1 min
38.5 sec; 1 min 36.9 sec; 1 min 37.2 sec; 1 min 36.5 sec; 1 min 38.7 sec; 1 min
37.0 sec. Find the average deviation and the 99% confidence interval for a
single value, expressing both as percentages.
20. The surface tension of a liquid may be determined by measuring the height to
which it will rise in a capillary of known radius. A student makes the following
observations of capillary rise with an unusual liquid that he has just prepared
in the laboratory: 63.2 mm; 63.5 mm; 62.9 mm; 62.8 mm; 63.7 mm; 63.4 mm.
Find the average deviation of these heights and the 90% confidence interval
for the mean, expressing both in parts per thousand.
21. How accurately should the values of liquid density and capillary radius be
known if all of the figures in the measurements in Problem 20 are to be
considered significant?
22. A graduated tube arranged to deliver variable volumes of a liquid is called a
buret. If a buret can be read to the nearest 0.01 ml, what total volume should
be withdrawn so that the volume will be known to a precision of 3 parts per
thousand? (Remember that two readings of the buret must be made for every
volume of liquid withdrawn.)
23. At some time or another, nearly everyone must decide whether to reject a
suspicious-looking result or to include it in the average of all the other results.
There is no agreement on what criteria should be used but, lacking information
about errors made in the experimental procedure, a rejection may be made on
the following statistical basis. If d and r are, respectively, the differences