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Business / Statistics for Business and Economics 12 / Chapter 6 / Problem 66E

Statistics for Business and Economics | 12th Edition | ISBN: 9780321826237 | Authors: James T. McClave, P. George Benson, Terry T Sincich

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If nothing is known about p, .5 can be substituted for p

Chapter 6, Problem 66E

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QUESTION:

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 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?

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QUESTION:

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 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?

ANSWER:

Solution:

Step 1 of 2:

It is given that nothing is known about p.

If we substitute p=0.5 in the sample size formula for population proportion a sample size larger than needed will be obtained.

Using this we need to find the circumstance under which the sample size will be larger than necessary.

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