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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? Useσ≈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 iszα/2=z0.05/2=z0.025=1.96

SE=zα/2σnn=z2α/2σ2SE2n=1.962×1221.52n=245.8624n≃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

Overbooking policies for major airlines.Airlines overbook flights to reduce the odds of flying with unused seats. An article in Transportation Research (Vol. 38, 2002) investigated the optimal overbooking policies for major airlines. One of the variables measured for each airline was the compensation (in dollars) per bumped passenger required to maximize future revenue. Consider the threshold compensation levels for a random sample of 10 major airlines shown in the next table. Estimate the true mean threshold compensation level for all major worldwide airlines using a90% confidence interval. Interpret the result practically.

825

850

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Who prepares your tax return? Refer to the Behavioral Research and Accounting (January 2015) study on income tax compliance, Exercise 5.50 (p. 321). Recall that in a sample of 270 U.S. adult workers, the researchers found that 37% prepare their own tax return.

a. Construct a 99% confidence interval for the true proportion of all U.S. adult workers who prepare their own tax return.

b. Suppose an IRS tax consultant claims that 50% of all U.S. adult workers prepare their own tax return. Make an inference about this claim.

c. According to the researchers, about 70% of the sampled workers were recruited from a shopping mall (where they were reimbursed $5 for their time) and about 30% were full-time workers enrolled in a professional graduate degree program. How might this information impact the inference you made in part b?

Lobster trap placement. Refer to the Bulletin of Marine Science (April 2010) observational study of teams fishing for the red spiny lobster in Baja California Sur, Mexico, Exercise 6.29 (p. 348). Trap-spacing measurements (in meters) for a sample of seven teams of red spiny lobster fishermen are repeated in the table. The researchers want to know how variable the trap-spacing measurements are for the population of red spiny lobster fishermen fishing in Baja California Sur, Mexico. Provide the researchers with an estimate of the target parameter using a 99% confidence interval.

Question: Furniture brand familiarity. A brand name that consumers recognize is a highly valued commodity in any industry. To assess brand familiarity in the furniture industry, NPD (a market research firm) surveyed 1,333 women who head U.S. households that have incomes of $25,000 or more. The sample was drawn from a database of 25,000 households that match the criteria listed above. Of the 10 furniture brands evaluated, La-Z-Boy was the most recognized brand; 70.8% of the respondents indicated they were “very familiar” with La-Z-Boy.

a. Describe the population being investigated by NPD.

b. In constructing a confidence interval to estimate the proportion of households that are very familiar with the La-Z-Boy brand, is it necessary to use the finite population correction factor? Explain.

c. What estimate of the standard error of should be used in constructing the confidence interval of part b?

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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?
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