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Chapter 6: Q66E (page 363)

If nothing is known about p, .5 can be substituted for p in the sample size formula for a population proportion. But when this is done, the resulting sample size may be larger than needed. Under what circumstances will be using p = .5 in the sample size formula yield a sample size larger than needed to construct a confidence interval for p with a specified bound and a specified confidence level?

Short Answer

Expert verified

Whenever p is greater than 0.5

Step by step solution

01

Given information

If nothing is known regarding p, 0.5 can be used in the sample size formula for a percentage of the population instead of p. However, the final sampling size may be greater than necessary if this is done.

02

Explanation

When p = 0.5, the sample size required is at its greatest.

As a result, if p is equivalent to 0.5, p=0.5, The sample size calculation will provide the needed sample size. However, if p is more than 0.5, use p=0.5. The sample size formula will provide a sample size more than what is needed to generate a confidence interval for p with a particular limit as well as a level of confidence.

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Most popular questions from this chapter

Radon exposure in Egyptian tombs. Refer to the Radiation Protection Dosimetry (December 2010) study of radon exposure in tombs carved from limestone in the Egyptian Valley of Kings, Exercise 6.30 (p. 349). The radon levels in the inner chambers of a sample of 12 tombs were determined, yielding the following summary statistics: x¯=3643Bq/m3and s=4487Bq/m3. Use this information to estimate, with 95% confidence, the true standard deviation of radon levels in tombs in the Valley of Kings. Interpret the resulting interval.

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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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?

Question: For the binomial sample information summarized in each part, indicate whether the sample size is large enough to use the methods of this chapter to construct a confidence interval for p.

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d. n = 20,p^= .3

Budget lapsing at army hospitals. Budget lapsing occurs when unspent funds do not carry over from one budgeting period to the next. Refer to the Journal of Management Accounting Research (Vol. 19, 2007) study on budget lapsing at U.S. Army hospitals, Exercise 2.113 (p. 126). Because budget lapsing often leads to a spike in expenditures at the end of the fiscal year, the researchers recorded expenses per full-time equivalent employee for each in a sample of 1,751 army hospitals. The sample yielded the following summary statistics:x¯=\(6,563 and s=\)2,484. Estimate the mean expenses per full-time equivalent employee of all U.S. Army hospitals using a 90% confidence interval. Interpret the result.

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