Sample size for interval estimate - Statistics
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Sample size for interval estimate - Statistics

[From: ] [author: ] [Date: 12-02-11] [Hit: ]
But your assumption of range/4 leads to a larger planning estimate for the std dev, and thus is more conservative (leads to larger sample size needed) - so I think range/4 is to be preferred here.......
This is my homework problem. Just wondering if I solved it correctly.

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $30,000 and $45,000. Assume 95% confidence interval estimate of the population mean annual starting salary is desired. What is the planning value for the population standard deviation? How large a sample should be taken if the desired margin of error is:

a. $500
b. $200
c. $100

My answers:

Planning value: (range/4) = (15,000/4) = 3,750

a. [(1.96²)(3750²)] / (500²) = 217

b. same as above but replaced 500² with 200² = 1351

c. same as above but replaced 200² with 100² = 5403

Am I correct? Thank you for any input!

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the approach and calculations are correct. Only comment is that sometimes I see as estimate of the std dev from the range to be range/6 ( assuming +/- 3 std dev). But your assumption of range/4 leads to a larger planning estimate for the std dev, and thus is more conservative (leads to larger sample size needed) - so I think range/4 is to be preferred here.
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