1. Copyright © Texas Education Agency, 2012. All rights reserved. Confidence Intervals Statistics & Risk Management 1 Copyright © Texas Education Agency, 2012. All rights reserved.

2. 2 “Copyright and Terms of Service Copyright © Texas Education Agency. The materials found on this website are copyrighted © and trademarked ™ as the property of the Texas Education Agency and may not be reproduced without the express written permission of the Texas Education Agency, except under the following conditions: 1)Texas public school districts, charter schools, and Education Service Centers may reproduce and use copies of the Materials and Related Materials for the districts’ and schools’ educational use without obtaining permission from the Texas Education Agency; 2) Residents of the state of Texas may reproduce and use copies of the Materials and Related Materials for individual personal use only without obtaining written permission of the Texas Education Agency; 3) Any portion reproduced must be reproduced in its entirety and remain unedited, unaltered and unchanged in any way; 4) No monetary charge can be made for the reproduced materials or any document containing them; however, a reasonable charge to cover only the cost of reproduction and distribution may be charged. Private entities or persons located in Texas that are not Texas public school districts or Texas charter schools or any entity, whether public or private, educational or non-educational, located outside the state of Texas MUST obtain written approval from the Texas Education Agency and will be required to enter into a license agreement that may involve the payment of a licensing fee or a royalty fee. Call TEA Copyrights with any questions you have.

3. Copyright © Texas Education Agency, 2012. All rights reserved. RandomSample Random Sample Sometimes we need to understand the characteristics of the larger picture. Sometimes we need to understand the characteristics of the larger picture. We may take a sample set of data that may infer what a larger population is, will think, do, or say. We may take a sample set of data that may infer what a larger population is, will think, do, or say. 3

4. Copyright © Texas Education Agency, 2012. All rights reserved. Assumptions When we collect sample data, it can be assumed that the data is in the form of a normal distribution. When we collect sample data, it can be assumed that the data is in the form of a normal distribution. The larger the sample, the more likely is will be a normal distribution. The larger the sample, the more likely is will be a normal distribution. It will be Symmetric and Uni-modal and often referred to as “Bell Shaped”. It will be Symmetric and Uni-modal and often referred to as “Bell Shaped”. 4

5. Copyright © Texas Education Agency, 2012. All rights reserved. NormalDistribution Normal Distribution 5

6. Copyright © Texas Education Agency, 2012. All rights reserved. Skewed Right 6

7. Copyright © Texas Education Agency, 2012. All rights reserved. Skewed Left 7

8. Copyright © Texas Education Agency, 2012. All rights reserved. Bimodal 8

9. Kurtosis 9

10. Outliers Some data scores do not fit the Normal Distribution. Some data scores do not fit the Normal Distribution. Trimmed Sample both ends to eliminate extremes Trimmed Sample both ends to eliminate extremes Winsorized Sample replace the trimmed scores with the closest normal scores. Winsorized Sample replace the trimmed scores with the closest normal scores. 10