Deanna is the principal at a Midwestern middle school and wants to know the average IQ of all female, seventh grade students. She does not know anything about what the population distribution looks like. She took a simple random sample of 31 seventh-grade girls in her school and found the average IQ score in her sample was 105.8 and the standard deviation was 15. Using the sample standard deviation above to estimate the population standard deviation, what is the minimum sample size needed for a 99.5% confidence interval to have a margin of error of no more than 2.3?

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Deanna is the principal at a Midwestern middle school and wants to know the average IQ of all female, seventh grade students.  She does not know anything about what the population distribution looks like.  She took a simple random sample of 31 seventh-grade girls in her school and found the average IQ score in her sample was 105.8 and the standard deviation was 15.

Using the sample standard deviation above to estimate the population standard deviation, what is the minimum sample size needed for a 99.5% confidence interval to have a margin of error of no more than 2.3?

 

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