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Chapter 6: Q68E (page 363)

Accounting and Machiavellianism. Refer to the Behavioral Research in Accounting(January 2008) study ofMachiavellian traits in accountants, Exercise 6.19 (p. 341),where a Mach rating score was determined for each ina sample of accounting alumni who work as purchasingmanagers. Suppose you want to reduce the width of the95% confidence interval for the true mean Mach ratingscore of all purchasing managers you obtained in Exercise 6.19b. How many purchasing managers should be includedin the sample if you desire a sampling error of only 1.5Mach rating points? Use蟽鈮�12 in your calculations.

Short Answer

Expert verified

246 purchasing managers should be includedin the sample if you desire a sampling error of only 1.5

Step by step solution

01

Given information

Referring to Exercise 6.19 (p. 341),

02

 Step 2: Finding the sample size

Here the standard error is 1.5

The value of the standard deviation is 12

The critical value for a 95% confidence interval isz伪/2=z0.05/2=z0.025=1.96

SE=z伪/2蟽nn=z2伪/2蟽2SE2n=1.962脳1221.52n=245.8624n鈮�246

246 purchasing managers should be includedin the sample if you desire a sampling error of only 1.5

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Most popular questions from this chapter

Crude oil biodegradation. Refer to the Journal of Petroleum Geology (April 2010) study of the environmental factors associated with biodegradation in crude oil reservoirs, Exercise 2.29 (p. 85). One indicator of biodegradation is the level of dioxide in the water. Recall that 16 water specimens were randomly selected from various locations in a reservoir on the floor of a mine and the amount of dioxide (milligrams/liter) as well as presence of oil was determined for each specimen. These data are reproduced in the next table.

a. Estimate the true mean amount of dioxide present in water specimens that contain oil using a 95% confidence interval. Give a practical interpretation of the interval.

b. Repeat part a for water specimens that do not contain oil.

c. Based on the results, parts a and b, make an inference about biodegradation at the mine reservoir.

Improving the productivity of chickens. Farmers have discovered that the more domestic chickens peck at objects placed in their environment, the healthier and more productive the chickens seem to be. White string has been found to be a particularly attractive pecking stimulus. In one experiment, 72 chickens were exposed to a string stimulus. Instead of white string, blue-colored string was used. The number of pecks each chicken took at the blue string over a specified time interval was recorded. Summary statistics for the 72 chickens were x = 1.13 pecks, s = 2.21 pecks (Applied Animal Behavior Science, October 2000).

a. Estimate population mean number of pecks made by chickens pecking at blue string using a 99% confidence interval. Interpret the result.

b. Previous research has shown that = 7.5 pecks if chickens are exposed to white string. Based on the results, part a, is there evidence that chickens are more apt to peck at white string than blue string? Explain.

Wear-out of used display panels. Refer to Exercise 4.126 (p. 270) and the study of the wear-out failure time of used colored display panels purchased by an outlet store. Recall that prior to acquisition, the panels had been used for about one-third of their expected lifetimes. The failure times (in years) for a sample of 50 used panels are reproduced in the table. An SPSS printout of the analysis is shown below.

a. Locate a 95% confidence interval for the true mean failure time of used colored display panels on the printout.

b. Give a practical interpretation of the interval, part a.

c. In the repeated sampling of the population of used colored display panels, where a 95% confidence interval for the mean failure time is computed for each sample, what proportion of all the confidence intervals generated will capture the true mean failure time?

Suppose N= 10,000, n= 2,000, and s= 50.

a. Compute the standard error of xusing the finite populationcorrection factor.

b. Repeat part a assuming n= 4,000.

c. Repeat part a assuming n= 10,000.

d. Compare parts a, b, and c and describe what happens to the standard error of xas nincreases.

e. The answer to part c is 0. This indicates that there is no sampling error in this case. Explain.

Preventing the production of defective items. It costs more toproduce defective items鈥攂ecause they must be scrappedor reworked鈥攖han 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 渭be 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?
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