Counting Statistics

Question 1

Systematic errors produce results that

Answer 1

differ consistently from the correct result by some fixed amount (inaccurate)

Question 2

Random errors are variations in results

Answer 2

from one measurement to the next, arising from physicial limitations of the system or from actual random variations of the quantity being measured

Question 3

_________ errors are always present in radiation counting and other measured data

Answer 3

random

Question 4

The percentage uncertainty is calculated by

Answer 4

Question 5

Confidence interval with 1 σ

Answer 5

68.3%

Question 6

Confidence interval with 2 σ

Answer 6

95%

Question 7

Confidence interval with 3 σ

Answer 7

99.7 %

Question 8

For radiation counting measures, the standard deviation is approximately

Answer 8

Question 9

The Gaussian and Poisson distributions are very close with then number of samples is

Answer 9

> 10

Question 10

For a series of counting measurements with individual results N1, N2, N3,

σ =

Answer 10

the square root of the sum of the squares of individual standard deviations

Question 11

For counting rate (R), the uncertainty σ is

Answer 11

Question 12

The percentage uncertainty in the count rate (R) is

Answer 12

Question 13

For two counting rates, for example comparing the difference, the total uncertainty is

Answer 13

square root of sum of squares of individual count rates

Question 14

The uncertainty and percentage uncertainty in a count rate and a background count rate are

Answer 14

Question 15

The minimum detectable activity of a radionuclide (statistically significant with a counting rate increase of 3σ)

Answer 15

3 x uncertainty of background count rate

Question 16

Two problems caused by high count rates

Answer 16

1. High background counting rates are undesirable because they increase uncertainties in net sample counting rates
2. Small differences between relatively high counting rates can have relatively large uncertainties

Question 17

The estimated counting time (knowing the approximate net and sample counting rates, R’s and R’b)

Answer 17

Question 18

Dividing the counting time most effectively to minimize the statistical error, the ratio of t1 and t2 relative to the counting rates R1 and R2 is

Answer 18

Question 19

Chi-squared (χ²) can be calculated as

Answer 19

(n-1)σ² / mean

or

Question 20

In a Chi-squared test, P refers to the probability that random variations observed in a series of n measurements

Answer 20

equal or exceed the χ² value

Question 21

In general for a chi-squared test, p-values within the range of _____________ are considered acceptable

Answer 21

.05 to .95

(staying within the expected range of deviations)