Chapter 4: Random Errors in Chemical Analysis

Question 1

these types of errors are caused by the many uncontrollable variables that accompany every measurement.

Answer 1

random errors

Question 2

TRUE or FALSE
Usually, most contributors
to random error cannot be positively identified. Even if we can identify random error sources, it is often impossible to measure them because most are so small that they cannot be detected individually

Answer 2

TRUE

Question 3

A ____________ is a bar graph such as
that shown by plot A

Answer 3

histogram

Question 4

is a curve that shows the symmetrical
distribution of data around the mean
of an infinite set of data

Answer 4

Gaussian, or normal error, curve

Question 5

The frequency distribution data is plotted as a

Answer 5

bar graph or histogram

Question 6

sources of random uncertainties in the calibration of a pipet

Answer 6

visual judgments
variations in drainage time & drainage angle
temperature fluctuations
vibrations and drafts

Question 7

Experiments in which the outcome
is either a success or failure are
binomial experiments that follow a

Answer 7

binomial distribution

Question 8

occurs for a series of
discrete events where the average
time between events is known, but
the exact timing is random.

Answer 8

Poisson distribution

Question 9

is the collection of
all measurements of interest to the
experimenter

Answer 9

population

Question 10

is a subset of measurements selected from
the population.

Answer 10

sample

Question 11

TRUE or FALSE
Generally, we base statistical analyses on the assumption that random errors in analytical results follow a Gaussian, or normal, distribution. Also, analytical data can follow other distributions other than the Gaussian distribution.

Answer 11

TRUE

Question 12

experiments in which there is either a successful outcome or a failure produce data that follow the

Answer 12

binomial distribution

Question 13

Radioactive or photon-counting experiments produce results that follow the

Answer 13

Poisson distribution

Question 14

is the collection of all measurements of interest and must be carefully defined by the experimenter. In some cases, it is defined as finite and real, while in others, it is hypothetical or conceptual in nature

Answer 14

population

Question 15

TRUE or FALSE
Typically in a scientific study, we infer information about a population or universe from observations made on a subset or sample.

Answer 15

TRUE

Question 16

refers to quantities such as m and s that define a population or distribution

Answer 16

parameter

Question 17

refers to an estimate of
a parameter that is made from a sample of data

Answer 17

statistic

Question 18

Example of statistics that estimate parameter

Answer 18

sample mean
sample standard deviation

Question 19

the arithmetic average of a limited sample drawn from a population of data

Answer 19

sample mean

Question 20

is defined as the sum of the measurement values divided by the number of measurements as given

Answer 20

sample mean

Question 21

is defined as the true mean for the population

Answer 21

population mean

Question 22

TRUE or FALSE
If there is no systematic error in the population, the population mean is also the true value for the measured quantity

Answer 22

TRUE

Question 23

TRUE or FALSE
the sample mean x is a statistic that estimates the population parameter m.

Answer 23

TRUE

Question 24

is a measure of the precision of the
population is given by summing the squares of the deviations from the mean, dividing by the number of measurements N, and taking the square root of the result

Answer 24

population standard deviation

Question 25

normal error curve has several general properties including

Answer 25

mean occurs at the central point of max frequency symmetrical distribution of positive and negative deviations about the maximum exponential decrease in frequency as magnitude of the deviations increases

Question 26

square of the standard deviation in a population is caled as

Answer 26

variance

Question 27

square of the standard deviation in a sample is caled as

Answer 27

sample variance

Question 28

indicates the number of independent results that enter into the computation of the standard deviation. It is also represented as N-1.

Answer 28

number of degrees of freedom

Question 29

TRUE or FALSE When m is unknown, two quantities must be extracted from a set of replicate data: x and s.

Answer 29

TRUE

Question 30

TRUE or FALSE never round a standard deviation calculation until the very end.

Answer 30

TRUE

Question 31

TRUE or FALSE As N becomes larger, x and s become better estimators of m and s.

Answer 31

TRUE

Question 32

The standard deviation of each mean is known as the

Answer 32

standard error of the mean (Sm)

Question 33

TRUE or FALSE The standard error of a mean, sm, is the standard deviation of a set of data divided by the square root of the number of data points in the set.

Answer 33

TRUE

Question 34

TRUE or FALSE If we have several subsets of data, a better estimate of the population standard deviation can be obtained by pooling (combining) the data instead of using only one data set.

Answer 34

TRUE

Question 35

is a weighted average of the individual estimates.

Answer 35

Spooled

Question 36

is just the square of the standard deviation

Answer 36

variance

Question 37

is an estimate of the population variance

Answer 37

sample variance

Question 38

TRUE or FALSE The advantage of using variance is that variances are additive in many situations,

Answer 38

TRUE

Question 39

formula for relative standard deviation

Answer 39

RSD= st= s/mean

Question 40

RSD multiplied by 100% is called the

Answer 40

coefficient variation

Question 41

is another term that is sometimes used to describe the precision of a set of replicate results. It is the difference between the largest value in the set and the smallest

Answer 41

spread or range

Question 42

TRUE or FALSE the absolute standard deviation of the logarithm of a number is determined by the relative standard deviation of the number; conversely, the relative standard deviation of the antilogarithm of a number is determined by the absolute standard deviation of the number

Answer 42

TRUE

Question 43

The__________ in a number are all the certain digits plus the first uncertain digit

Answer 43

significant figures

Question 44

TRUE or FALSE It is especially important to postpone rounding until the calculation is completed

Answer 44

TRUE

Question 45

At least one extra digit beyond the significant digits should be carried through all the computations in order to avoid a rounding error, which is called

Answer 45

guard digit