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Description: When an audit must be conducted that involves a tedious examination of a large inventory, the audit may be very costly and time consuming if each item in the inventory must be examined. In such situations, the auditor frequently obtains a random samp

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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When an audit must be conducted that involves a tedious examination of a large inventory, the audit may be very costly and time consuming if each item in the inventory must be examined. In such situations, the auditor frequently obtains a random sample of items from the complete inventory and uses the results of an audit of the sampled items to check the validity of the company's financial statement. A large company’s financial statement claims an inventory that averages $600 per item. The following data are the auditor’s assessment of a random sample of 75 items from the company’s inventory. The values resulting from the audit are rounded to the nearest dollar.

Estimate the mean value of an item in the inventory using a 95% confidence interval.
Is there substantial evidence (a 5 .01) that the mean value of an item in the inventory is less than $600?
What is the target population for the above inferences?
Would normal distribution–based procedures be appropriate for answering the above questions?

303
547
1,368
493
984
507
148 2,546
738
83
2
135
274
74
1,472
399
1,784 71
751
136
571
147
282
2,039
1,909
748
188
548
1
280
102
618
129
1,324 1,428 469
102 454
1,059
939
303
600
234
514
17
1,290 685
3,215 | 3
551
293
1,395
7
28
973
506
511
812
447
11
35
252
1,526
464
67
99
67
259
7
67
248
33
41

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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