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Chapter 6: Q71E (page 364)

Do social robots walk or roll? Refer to the InternationalConference on Social Robotics(Vol. 6414, 2010) studyof the trend in the design of social robots, Exercise 6.48(p. 357). Recall that you used a 99% confidence interval toestimate the proportion of all social robots designed withlegs, but no wheels. How many social robots would need tobe sampled in order to estimate the proportion to within.075 of its true value?

Short Answer

Expert verified

286 social robots would need to be sampled in order to estimate the proportion to within.075 of its true value

Step by step solution

01

Given information

Referring to Exercise 6.48(p. 357).

02

Finding the sample size

Here the sample proportionp^=63106=0.59

q^=1鈭�p^=1鈭�0.59434=0.41

Here the standard error is 0.075

The critical value for a 99% confidence interval isz伪/2=z0.01/2=z0.005=2.576

SE=z伪/2p^q^nn=z2伪/2p^q^SE2n=2.5762脳0.59脳0.410.0752n=285.37n鈮�286

The required sample size is 286

286 social robots would need to be sampled in order to estimate the proportion to within.075 of its true value

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Most popular questions from this chapter

Study of aircraft bird-strikes. As worldwide air traffic volume has grown over the years, the problem of airplanes striking birds and other flying wildlife has increased dramatically. The International Journal for Traffic and Transport Engineering (Vol. 3, 2013) reported on a study of aircraft bird strikes at Aminu Kano International Airport in Nigeria. During the survey period, a sample of 44 aircraft bird strikes were analyzed. The researchers found that 36 of the 44 bird strikes at the airport occurred above 100 feet. Suppose an airport air traffic controller estimates that less than 70% of aircraft bird strikes occur above 100 feet. Comment on the accuracy of this estimate. Use a 95% confidence interval to support your inference.

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.

A random sample of 90 observations produced a mean x = 25.9 and a standard deviation s = 2.7.

a. Find an approximate 95% confidence interval for the population mean渭

b. Find an approximate 90% confidence interval for渭

c. Find an approximate 99% confidence interval for渭

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

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 鈥淢ade in the USA鈥� 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 鈥�90% confidence鈥� means for this interval.

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

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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