Cia Part I - Su 5.4 Variables Sampling

Front 1

For what kind of variables is variables sampling used for?

Back 1

continuous variables

Front 2

what kind of information does variables sampling provide?

Back 2

whether a stated amount (balance of account receivables) is materially misstated after the IA has determined the confidence INTERVAL around the sample result that includes the true (but unknown) value at a specified confidence level

Front 3

On which four factors does the sample size in classical variables sampling depend?

Back 3

- confidence level (i.e. confidence coefficient)

- standard deviation of errors in the preliminary sample

- population size (number of items in the population)

- tolerable error (i.e. materiality)

- anticipated error

Front 4

What is the formula for sample size for classical variables sampling?

Back 4

Front 5

What are the 4 statistical sampling methods based on equal probability selection?

Back 5

- mean per unit (MPU)

- stratified MPU

- ratio estimation

- difference estimation

Front 6

What are the four working steps in MPU and ratio estimation sampling methods?

Back 6

- projection of sample error to the population (EE)

- calculation of precision (SE)

- determination of upper limit of error

(ULE = EE + SE)

- evaluation: comparison of ULE with maximum tolerable error

Front 7

How large is the projected error of the population according to the mean-per-unit estimation method, if a sample of 10 (out of 200) accounts with a recorded amount of $60 (total recorded amount is $2000) is audited, and based on the sample the total amount of the 10 accounts is $50?

Back 7

- average error per sample item: ($60-$50)/10=$1

- projected error: 200x$1=$200

Hint 7

Front 8

How large is the projected error of the population according to the the ratio estimation method, if a sample of 10 (out of 200) accounts with a recorded amount of $60 (total recorded amount is $2000) is audited, and based on the sample the total amount of the 10 accounts is $50?

Back 8

- sample error rate : ($60-$50)/60=16,7%

- projected error: 16,7%x$2000=$334

Hint 8

Front 9

What does MPU project for a population according to Wiley and Gleim? Provide an example for: population size 100, sample size 10, recorded amount of the samples 1000, audited amount of the samples 1500

Back 9

a total dollar value for a population

projected population value (1500/10)*100=15000

Front 10

What does ratio estimation project for a population according to Wiley and Gleim? Provide an example for: population's recorded value 10000, sample size 10, recorded amount of the samples 1000, audited amount of the samples 1500

Back 10

a total dollar value for a population

(1500/1000)*10000= 15000

Front 11

When can the decision be made in the sampling process which projection method to employ?

Back 11

after the sample is selected and audited

Front 12

What is the formula for achieved precision in classical variables sampling?

Back 12

Front 13

How is the upper limit of error (ULE=EE+SE)) compared with the maximum tolerable error (TE)?

Back 13

Hint 13

Front 14

What is a stratified MPU estimation?

Back 14

MPU estimation based on a group of items that was separated from the total population due to the group's lesser variability than in the whole population

Front 15

Which criteria are appropriate for stratification in variables sampling?

Back 15

generally all variables that may explain the level of error in the population (especially monetary values)

Front 16

What is the stratified MPU good for?

Back 16

to increase audit efficiency by reducing the variability within each group and allowing for a smaller overall sample size

Front 17

According to Wiley, to which stratum should the largest portion of the overall sample size be allocated in simple random sampling?

Back 17

to the stratum with the largest standard deviation

Front 18

According to EU Commission, to which stratum should the largest portion of the overall sample size be allocated in simple random sampling?

Back 18

to the stratum with the largest population

Front 19

How large is the projected error of the population according to the difference estimation method, if a sample of 10 (out of 200) accounts with a recorded amount of $60 (total recorded amount is $2000) is audited, and based on the sample the total amount of the 10 accounts is $50?

Back 19

- average error per sample item: ($60-$50)/10=$1

- projected error: 200x$1=$200

Front 20

What are the 4 working steps according to the difference estimation method after the projection of the sample error to the population to evaluate the sample results?

Back 20

- projection for the correct book value (CBV)

- calculation of precision (SE)

- calculation of the lower limit (LL=CBV-SE)

- comparison of CBV and LL with BV-TE

Front 21

How are the correct book value (CBV) projected and the precision (SE) calculated?

Back 21

Front 22

Which 4 factors do affect the size of the achieved precision and how do they affect it if these factors are increased?

Back 22

- the larger the confidence level (i.e. confidence coefficient), the higher the achieved precision

- the larger the sample errors' standard deviation, the higher the achieved precision

- the larger the population's size, the higher the achieved precision

- the larger the sample size, the lower the achieved precision

Front 23

What can be concluded from the comparison of the corrected book value (CBV) and the lower limit (LL) with the book value (BV) reduced by the tolerable error (TE)?

Back 23

Hint 23

Front 24

What does difference estimation project for a population according to Wiley and Gleim? Provide an example for: population's recorded value 10000, populations size 100, sample size 10, recorded amount of the samples 1000, audited amount of the samples 1500

Back 24

the estimated correct value of the population

error per sample item (1500 - 1000)/10=50

projected error 50 * 100=5000

estimated correct population value 10000+5000=15000

Front 25

If the corrected book value (CBV) is 1000, the calculated precision is 100, and the confidence level 95%, what is the probability that the true (but unknow) value is lower than 900 or higher than 1100?

Back 25

2,5% in each case =(100%-95%)/2

Front 26

Which precision limit (upper or lower limit) is an IA concerned about in variables sampling?

Back 26

upper and lower limit (a receivables balance can be either over- or understated)

Front 27

If the sample mean per sampled inventory is $52 and the achieved precision per unit is $1.03, what is the estimated inventory value for 20,000 inventory item? Is the estimated value within the desired precision of 2%?

Back 27

confidence interval of estimated inventory value: 20,000x(52+-1.03)= $1,019,400 and 1,060,600

achieved precision: $1,03/$52=1,98% < 2%

Front 28

How does monetary-unit sampling (MUS) work?

Back 28

- the sampling unit is a unit of money ( a HOMOGENOUS unit) rather than an invoice or an account

- an item (invoice, account, etc.) containing the specific monetary unit is selected for testing

Front 29

What are the advantages of MUS?(2)

Back 29

- efficient sampling model for establishing that a low error rate population is not materially misstated

- does not require the normal distribution approximation required by variable sampling

Front 30

Which method of sample selection is used for MUS?

Back 30

systematic sample selection method with probability proportional to size

Front 31

How is MUS called as well?

Back 31

probability-proportional-to-size (PPS)

Front 32

How large must the error rate in the population maximally be so that using MUS is still efficient?

Back 32

10%

Front 33

On which five factors does the sample size for MUS depend (according to EU commission)?

Back 33

- confidence level (i.e. confidence coefficient)

- population book value

- standard-deviation of error rates produced from a MUS sample

- maximum tolerable error

- anticipated error

Front 34

According to Gleim, on what does the sample size for MUS NOT depend?

Back 34

standard deviation of the book values or of the errors in the populaton

Front 35

What is the formula for MUS sample size?

Back 35

Front 36

How is the cut-off value for the high-value stratum in MUS determined in which all samples are audited?

Back 36

Front 37

Which sample selection method is used for MUS?

Back 37

systematic selection

Front 38

How is the sampling interval in MUS determined?

Back 38

Front 39

How must the population be arranged so that MUS can be used?

Back 39

cumulatively

Front 40

How are the first and the second sample items in MUS selected?

Back 40

Front 41

How is the projected error at the level of population calculated in MUS?

Back 41

Hint 41

49,464,419 = sampling interval 7,616,805 = total error amount in the high-value stratum (exhaustive stratum)

Front 42

How is precision calculated in MUS ?

Back 42

Front 43

How are the sampling results evaluated in MUS?

Back 43

Front 44

For which variables sampling methods must the recorded book value of the population items be known?

Back 44

- ratio estimation

- difference estimation

- MUS

- according to Gleim not for MPU (according to EU Commission book values are needed in MPU as well to calculate the error for each sample item)

Hint 44

Front 45

When should unstratified MPU be used?(2)

Back 45

- when only a few errors in the population are expected

- when there is an expectation that errors are relatively independent from the level of book values (higher errors can be found either in units of high or low level of book values)

Front 46

When may MPU sampling be difficult?

Back 46

in an unstratified sampling situation

Front 47

Which sampling methods are used when estimating dollar amounts of errors for normally distributed population?

Back 47

Difference or ratio estimation

Front 48

When should ratio estimation be used?(3)

Back 48

- errors can be found in the whole population(errors are not skewed)

- book values are highly variable

- when errors are proportional to book values (higher value items tend to exhibit higher errors)

Front 49

When is difference estimation useful?(4)

Back 49

- when it is intended to project the correct balance in the population

- errors can be found in the whole population (errors are not skewed)

- if the book values tend to be similar (low variability of book values)

- if the level of error is relatively constant in the population (errors are not proportional to book values)

Front 50

When is difference estimation preferable to ratio estimation?

Back 50

- when errors are not proportional

Front 51

When are ratio estimation and difference estimation not efficient?

Back 51

When only a few differences between recorded and observed amounts (errors) arefound

Front 52

When is MUS appropriate?(3)

Back 52

- when some items in account balances may be far larger (overstated) than others in the population (high variability of book values)

- when there is positive correlation between errors and book values

- when only a few errors are expected

Front 53

When is MUS inefficient?

Back 53

many misstatements (overandunderstatements) are expected

- when understatements and negative amounts are expected

Front 54

Which sampling methods are efficient if a high degree of variability in book values within the population prevails?(2)

Back 54

- ratio estimation

- MUS