Question Details

Auditors of Old Kent Bank are interested in comparing the reported value 


NARRBEGIN: SA_81_82
A battery manufacturer wants to estimate the average number of defective (or dead) batteries contained in a box shipped by the company. Production personnel at this company have recorded the number of defective batteries found in each of the 2000 boxes shipped in the past week.
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1.	(A) What sample size would be required for the production personnel to be approximately 95% sure that their estimate of the average number of defective batteries per box is within 0.3 unit of the true mean? Assume that the best estimate of the population standard deviation ( ) is 0.9 defective batteries per box.

(B) How does your answer to (A) change if the production personnel want their estimate to be within 0.5 unit of the actual population mean? Evaluate the tradeoff between required accuracy and sample size requirement for this case and the case in (A).




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Auditors of Old Kent Bank are interested in comparing the reported value of customer savings account balances with their own findings regarding the actual value of such assets. Rather than reviewing the records of each savings account at the bank, the auditors decide to examine a representative sample of savings account balances. The frame from which they will sample is shown below.


$75.30		$614.11		$696.34		$572.08
$748.23		$21.20		$99.79		$1,233.38
$530.40		$378.37		$596.14		$239.65
$2,995.38		$1,069.06		$929.80		$259.98
$123.65		$68.92		$192.35		$754.45
$309.00		$163.31		$71.75		$904.92
$40.70		$161.12		$459.38		$171.48
$402.81		$157.44		$41.81		$87.08
$489.97		$468.12		$400.57		$319.40
$533.82		$1,801.35		$1,666.50		$37.16
$85.92		$91.43		$193.14		$106.95
$214.62		$10.62		$582.18		$39.65
$123.66		$76.33		$291.73		$398.48
$659.18		$101.24		$1,740.47		$322.26
$1,509.34		$1,599.04		$358.62		$492.05
$1,052.68		$596.33		$100.54		$1,288.70
$421.46		$1,799.51		$581.21		$571.63
$180.58		$98.82		$358.68		$38.93
$874.78		$2,761.93		$750.44		$376.60
$269.48		$456.79		$216.81		$305.49

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	2.	(A) What sample size would be required for the auditors to be approximately 95% sure that their estimate of the average savings account balance at this bank is within $150 of the true mean? Assume that their best estimate of the population standard deviation   is $300.

(B) Choose a simple random sample of the size found in (A).	

(C) Compute the observed sampling error based on the sample you have drawn from the population. How does the actual sampling error compare to the maximum possible probable absolute error established in (A)? Explain




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