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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−p^=1−0.59434=0.41

Here the standard error is 0.075

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

SE=zα/2p^q^nn=z2α/2p^q^SE2n=2.5762×0.59×0.410.0752n=285.37n≈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

Interviewing candidates for a job. The costs associated with conducting interviews for a job opening have skyrocketed over the years. According to a Harris Interactive survey 211 of 502senior human resources, executives at U.S. companies believe that their hiring managers are interviewing too many people to find qualified candidates for the job (Business Wire, June 82006).

a.Describe the population of interest in this study.

b.Identify the population parameter of interest p.

c.Is the sample size large enough to provide a reliable estimate of p?

d.Find and interpret an interval estimate for the true proportion of senior human resources executives who believe that their hiring managers interview too many candidates during a job search. Use a confidence levelof 98%.

e.If you had constructed a90% confidence interval, would it be wider or narrower?

The following is a 90% confidence interval for p:(0.26, 0.54). How large was the sample used to construct thisinterval?

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.

Latex allergy in health care workers. Health care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Each sample of 46 hospital employees who were diagnosed with a latex allergy based on a skin-prick test reported their exposure to latex gloves (Current Allergy& Clinical Immunology, March 2004). Summary statistics for the number of latex gloves used per week is ,x¯=19.3

s = 11.9.

a. Give a point estimate for the average number of latex gloves used per week by all health care workers with a latex allergy.

b. Form a 95% confidence interval for the average number of latex gloves used per week by all health care workers with a latex allergy.

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

d. Give the conditions required for the interval, part b, to be valid.

Question: A random sample of n measurements was selected from a population with unknown meanμand known standard deviationσ2. Calculate a 95% confidence interval forαfor each of the following situations:

a. n = 75, X = 28,σ2= 12

b. n = 200, X= 102, σ2= 22

c. n = 100, X= 15,σ2=.3

d. n = 100, X= 4.05, σ2= .83

e. Is the assumption that the underlying population of measurements is normally distributed necessary to ensure the validity of the confidence intervals in parts a–d? Explain.
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