Assume that the sample is a simple random sample obtained from a normally distributed population of IQ scores of statistics professors. Use the table below to find the minimum sample size needed to be 95% confident that the sample standard deviation s is within 40% of sigma. Is this sample size​ practical? a. The minimum sample size needed is

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Assume that the sample is a simple random sample obtained from a normally distributed population of IQ scores of statistics professors. Use the table below to find the minimum sample size needed to be 95% confident that the sample standard deviation s is within 40% of sigma. Is this sample size​ practical?

a. The minimum sample size needed is

 

To be 95% confident that \( s \) is within a certain percentage of the value of \( \sigma \), the sample size \( n \) should be at least:

- For 1%: \( n = 19,205 \)
- For 5%: \( n = 768 \)
- For 10%: \( n = 192 \)
- For 20%: \( n = 48 \)
- For 30%: \( n = 21 \)
- For 40%: \( n = 12 \)
- For 50%: \( n = 8 \)

To be 99% confident that \( s \) is within a certain percentage of the value of \( \sigma \), the sample size \( n \) should be at least:

- For 1%: \( n = 33,218 \)
- For 5%: \( n = 1,336 \)
- For 10%: \( n = 336 \)
- For 20%: \( n = 85 \)
- For 30%: \( n = 38 \)
- For 40%: \( n = 22 \)
- For 50%: \( n = 14 \)
Transcribed Image Text:To be 95% confident that \( s \) is within a certain percentage of the value of \( \sigma \), the sample size \( n \) should be at least: - For 1%: \( n = 19,205 \) - For 5%: \( n = 768 \) - For 10%: \( n = 192 \) - For 20%: \( n = 48 \) - For 30%: \( n = 21 \) - For 40%: \( n = 12 \) - For 50%: \( n = 8 \) To be 99% confident that \( s \) is within a certain percentage of the value of \( \sigma \), the sample size \( n \) should be at least: - For 1%: \( n = 33,218 \) - For 5%: \( n = 1,336 \) - For 10%: \( n = 336 \) - For 20%: \( n = 85 \) - For 30%: \( n = 38 \) - For 40%: \( n = 22 \) - For 50%: \( n = 14 \)
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