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Chapter 6: Q91E (page 367)

Invoice errors in a billing system. In a study of invoice errors in a company’s new billing system, an auditor randomly sampled 35 invoices produced by the new system and recorded actual amount (A), invoice amount (I), and the difference (or error),x=A-I . The results were x¯=\(1ands=\)124. At the time that the sample was drawn, the new system had produced 1,500 invoices. Use this information to find an approximate 95% confidence interval for the true mean

Short Answer

Expert verified

The 95% confidence interval for true mean is (-40.92, 42.92).

Step by step solution

01

Given information

The population size is N=1500 invoices

The sample size is n = 35 invoices

The sample mean of invoices is x¯=$1

The standard deviation of the invoice iss=$124

02

Calculating a confidence interval

Consider,

nN=351500=0.02

Here, nN=0.02<0.05the finite population correction factor is not included in the calculation of the standard error.

The 95% confidence interval for the true mean is obtained by using the following formula,

x¯±2sn

Therefore,

x¯±2sn=1±212435=1±41.92=-40.92,42.92

Hence, the required confidence interval is (-40.92, 42.92), and it is 95% confident that the true mean invoice error of the new system is lies between -$40.92 and $42.92

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Most popular questions from this chapter

U.S. Postal Service’s performance. The U.S. Postal Service (USPS) reports that 95% of first-class mail within the same city is delivered on time (i.e., within 2 days of the time of mailing). To gauge the USPS performance, Price Waterhouse monitored the delivery of first-class mail items between Dec. 10 and Mar. 3—the most difficult delivery season due to bad weather conditions and holidays. In a sample of 332,000 items, Price Waterhouse determined that 282,200 were delivered on time. Comment on the performance of USPS first-class mail service over this time period.

Products “Made in the USA.” Refer to Exercise 2.154 (p. 143) and the Journal of Global Business (Spring 2002) survey to determine what “Made in the USA” means to consumers. Recall that 106 shoppers at a shopping mall in Muncie, Indiana, responded to the question, “Made in the USA” means what percentage of U.S. labor and materials?” Sixty-four shoppers answered,“100%.”

a. Define the population of interest in the survey.

b. What is the characteristic of interest in the population?

c. Estimate the true proportion of consumers who believe “Made in the USA” means 100% U.S. labor and materials using a 90% confidence interval.

d. Give a practical interpretation of the interval, part c.

e. Explain what the phrase “90% confidence” means for this interval.

f. Compute the sample size necessary to estimate the true proportion to within .05 using a 90% confidence interval.

Improving SAT scores. Refer to the Chance (Winter 2001) and National Education Longitudinal Survey (NELS) study of 265 students who paid a private tutor to help them improve their SAT scores, Exercise 2.88 (p. 113). The changes in both the SAT–Mathematics and SAT–Verbal scores for these students are reproduced in the table. Suppose the true population meansa change in score on one of the SAT tests for all students who paid a private tutor is 15. Which of the two tests, SAT–Mathematics or SAT–Verbal, is most likely to have this mean change? Explain.

Preventing the production of defective items. It costs more toproduce defective items—because they must be scrappedor reworked—than it does to produce non-defective items.This simple fact suggests that manufacturers shouldensurethe quality of their products by perfecting theirproduction processes rather than through inspection of finishedproducts (Out of the Crisis,Deming, 1986). In orderto better understand a particular metal-stamping process, the manufacturer wishes to estimate the mean length of itemsproduced by the process during the past 24 hours.

a. How many parts should be sampled in order to estimatethe population means to within .1 millimetre (mm)with 90% confidence? Previous studies of this machinehave indicated that the standard deviation of lengthsproduced by the stamping operation is about 2 mm.

b. Time permits the use of a sample size no larger than100. If a 90% confidence interval for is constructedusing n= 100, will it be wider or narrower than wouldhave been obtained using the sample size determined in

part a? Explain.

c. If management requires that μbe estimated to within.1 mm and that a sample size of no more than 100 beused, what is (approximately) the maximum confidencelevel that could be attained for a confidence interval

Does that meet management's specifications?

Calculate the finite population correction factor for each

of the following situations:

a. n = 50, N = 2,000

b. n = 20, N = 100

c. n = 300, N = 1,500
See all solutions

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