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 99​% confident that the sample standard deviation s is within 1% of sigma .Is this sample size​ practical

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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 99​% confident that the sample standard deviation s is within 1% of sigma .Is this sample size​ practical?

a. The minimum sample size needed is

 

 

### Sample Size Requirements for Estimating Standard Deviation

**σ:** Standard deviation

**To be 95% confident that s is within:**

- **1% of the value of σ**, the sample size \( n \) should be at least **19,205**
- **5% of the value of σ**, the sample size \( n \) should be at least **768**
- **10% of the value of σ**, the sample size \( n \) should be at least **192**
- **20% of the value of σ**, the sample size \( n \) should be at least **48**
- **30% of the value of σ**, the sample size \( n \) should be at least **21**
- **40% of the value of σ**, the sample size \( n \) should be at least **12**
- **50% of the value of σ**, the sample size \( n \) should be at least **8**

**To be 99% confident that s is within:**

- **1% of the value of σ**, the sample size \( n \) should be at least **33,218**
- **5% of the value of σ**, the sample size \( n \) should be at least **1,336**
- **10% of the value of σ**, the sample size \( n \) should be at least **336**
- **20% of the value of σ**, the sample size \( n \) should be at least **85**
- **30% of the value of σ**, the sample size \( n \) should be at least **38**
- **40% of the value of σ**, the sample size \( n \) should be at least **22**
- **50% of the value of σ**, the sample size \( n \) should be at least **14**
Transcribed Image Text:### Sample Size Requirements for Estimating Standard Deviation **σ:** Standard deviation **To be 95% confident that s is within:** - **1% of the value of σ**, the sample size \( n \) should be at least **19,205** - **5% of the value of σ**, the sample size \( n \) should be at least **768** - **10% of the value of σ**, the sample size \( n \) should be at least **192** - **20% of the value of σ**, the sample size \( n \) should be at least **48** - **30% of the value of σ**, the sample size \( n \) should be at least **21** - **40% of the value of σ**, the sample size \( n \) should be at least **12** - **50% of the value of σ**, the sample size \( n \) should be at least **8** **To be 99% confident that s is within:** - **1% of the value of σ**, the sample size \( n \) should be at least **33,218** - **5% of the value of σ**, the sample size \( n \) should be at least **1,336** - **10% of the value of σ**, the sample size \( n \) should be at least **336** - **20% of the value of σ**, the sample size \( n \) should be at least **85** - **30% of the value of σ**, the sample size \( n \) should be at least **38** - **40% of the value of σ**, the sample size \( n \) should be at least **22** - **50% of the value of σ**, the sample size \( n \) should be at least **14**
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