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 50% of sigma.

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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 50% of sigma. 

a. The minimum sample size needed is

### Sample Size Requirements for Estimating the Population Standard Deviation

This table outlines the minimum sample sizes needed to be confident that the sample standard deviation (s) falls within a certain percentage of the population standard deviation (σ). The confidence levels considered are 95% and 99%.

#### 95% Confidence Level:
- **1%** of σ: Sample size should be at least **19,205**
- **5%** of σ: Sample size should be at least **768**
- **10%** of σ: Sample size should be at least **192**
- **20%** of σ: Sample size should be at least **48**
- **30%** of σ: Sample size should be at least **21**
- **40%** of σ: Sample size should be at least **12**
- **50%** of σ: Sample size should be at least **8**

#### 99% Confidence Level:
- **1%** of σ: Sample size should be at least **33,218**
- **5%** of σ: Sample size should be at least **1,336**
- **10%** of σ: Sample size should be at least **336**
- **20%** of σ: Sample size should be at least **85**
- **30%** of σ: Sample size should be at least **38**
- **40%** of σ: Sample size should be at least **22**
- **50%** of σ: Sample size should be at least **14**
Transcribed Image Text:### Sample Size Requirements for Estimating the Population Standard Deviation This table outlines the minimum sample sizes needed to be confident that the sample standard deviation (s) falls within a certain percentage of the population standard deviation (σ). The confidence levels considered are 95% and 99%. #### 95% Confidence Level: - **1%** of σ: Sample size should be at least **19,205** - **5%** of σ: Sample size should be at least **768** - **10%** of σ: Sample size should be at least **192** - **20%** of σ: Sample size should be at least **48** - **30%** of σ: Sample size should be at least **21** - **40%** of σ: Sample size should be at least **12** - **50%** of σ: Sample size should be at least **8** #### 99% Confidence Level: - **1%** of σ: Sample size should be at least **33,218** - **5%** of σ: Sample size should be at least **1,336** - **10%** of σ: Sample size should be at least **336** - **20%** of σ: Sample size should be at least **85** - **30%** of σ: Sample size should be at least **38** - **40%** of σ: Sample size should be at least **22** - **50%** of σ: Sample size should be at least **14**
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