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Answered) MISCELLANEOUS STATISTICAL SAMPLING PROBLEMS THE POPULATION, THE FRAME AND THE SAMPLING UNIT The following problems are based on the material in the...

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MISCELLANEOUS STATISTICAL SAMPLING PROBLEMS THE POPULATION, THE FRAME AND THE SAMPLING UNIT

The following problems are based on the material in the ELEMENTS OF SAMPLING: THE

POPULATION, THE FRAME AND THE SAMPLING UNIT folder.

The problems refer to the Revised Sales-AR-Receipts Manual System flowchart, which is in

INTERNAL CONTROL > SALES-ACCOUNTS RECEIVABLE > MANUAL SYSTEM.

For each of the following test objectives, identify: The assertion The population The frame The sampling unit Supporting document[s]

1. Recorded sales are posted timely

2. Shipments are billed

3. Recorded sales occured 1 MISCELLANEOUS STATISTICAL SAMPLING PROBLEMS INTERPRETING SAMPLE RESULTS

The following problems are based on the material in the INTERPRETING CONFIDENCE

INTERVALS IN AUDIT SAMPLES folder. Your best approach to proper interpretation is to sketch

the results on a 1-dimensional graph.

1. An auditor has selected and evaluated a statistical sample of accounts receivable to assess

collectibility on an account-by-account basis, and then project the finding of uncollectible

amounts to the population. Several accounts were found in the examination to be partly or

entirely uncollectible.

The test results showed that, at 95% confidence, uncollectible receivables total between

800,000 and 4,200,000 (overstatement).

a. What should be the auditor's conclusion if the maximum tolerable misstatement is

$1,800,000?

b. Propose an appropriate adjusting journal entry.

c. Suppose that, prior to this test, the client's allowance for uncollectible accounts is $1,000,000.

What would you recommend?

2. You are performing an obsolescence review of a 22,000 item parts inventory. The book value

of the inventory is $10,515,000. You decide to select a random sample for dollar value

estimation. The maximum tolerable misstatement is $500,000 and the planned confidence level

is 95% (2-sided). Pricing errors were disclosed in the sample.

What would be your conclusions/recommendation in each of the following situations?

a. Overstated by an estimated $320,000, with a lower confidence limit [LCL] of $30,000 and an

upper confidence limit [UCL] of $610,000.

b. Overstated by an estimated $240,000, with LCL = $90,000 and UCL=$390,000. $ VALUE ESTIMATION â€“ DESIGN AND EVALUATION

The following problems are based on the material in the VARIABLES ESTIMATION IN EQUAL

PROBABILITY SAMPLES folder. 2 MISCELLANEOUS STATISTICAL SAMPLING PROBLEMS

1. An equal probability random sample of 432 items was selected from a population of

11,487 items. The average value of the sample was $127.09, and its standard deviation

was $42.08. Calculate the 99% confidence interval. 2. An equal probability random sample of 110 items was selected from a population of 5,230

items. The sample disclosed six misstated items, and 104 items with $0.00 misstatement.

The amounts of the misstatements are as follows:

Misstatement

$ 235.30

(147.33)

24.35

101.21

( 18.04)

92.55

$ 288.04 net overstatement

Calculate the 95% two-sided confidence interval on the total misstatement in the

population. [Hint: Do not ignore the items with $0 misstatement] 3. If a population has a total value of $5,724,300, a standard deviation of $840, and a

population size of 15,000 items, what is the probability that a simple random

sample of 1,500 items will yield an estimate of the population's total value that is

within 10% of the actual total value? 4. If a population has 94,000 items and an estimated standard deviation of $235, how large a

sample would be required to estimate the population's total value to within $2,000,000 of

its value? Assume a 90% two-sided confidence level. ANSWERS

1. Lower limit Upper limit

$1,399,712 $15,20053 [without finite population correction]

2. Lower limit Upper limit

($15,643) $43,033 [without finite population correction]

3. Within +/- 10%, probability = 0.9364

4. Within +/- $2,000,000, sample size = 331

HYPOTHESIS TESTING

The following problems are based on the materials in the AUDIT SAMPLING AND HYPOTHESIS

TESTING folder. 3 MISCELLANEOUS STATISTICAL SAMPLING PROBLEMS

1. A random sample is to be selected from a population of 22,000 items. The standard error the

estimate of the populationâ€™s total value [ Ïƒ T^ ] is $78,500. If the chosen confidence level [1 is 95%, what is the risk [] of failing to detect misstatement amounting to $100,000?

(Hint: First, calculate the precision [A])

2. Given that the maximum tolerable misstatement is $750000 and the risk of incorrect

rejection (estimation risk) is 20%, calculate the required precision for the following detection

risks []: 10%, and 50%.

3. Given that materiality is $700000, planned precision is $500000, and confidence level is 90%,

calculate the risk of accepting a materially misstated book value.

ANSWERS:

1. 75.4% risk of failing to detect $100,000

2. Risk

Precision

10%

$277,479

50%

$700,000

3. Probability of accepting materially misstated book value is 25.5% 4

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