7.2 Confidence Intervals When SD is unknown. The value of , when it is not known, must be estimated by using s, the standard deviation of the sample.

Slides:

Advertisements

Similar presentations

Chapter 6 Confidence Intervals.

Advertisements

Estimating a Population Variance

© The McGraw-Hill Companies, Inc., Chapter 8 Confidence Intervals and Sample Size.

Normal Probability Distributions 1 Chapter 5. Chapter Outline Introduction to Normal Distributions and the Standard Normal Distribution 5.2 Normal.

Confidence Interval Estimation of Population Mean, μ, when σ is Unknown Chapter 9 Section 2.

Confidence Intervals and Sample Size

Chapter Topics Confidence Interval Estimation for the Mean (s Known)

Estimating  When  Is Unknown

Confidence Intervals Confidence Interval for a Mean

1 (Student’s) T Distribution. 2 Z vs. T Many applications involve making conclusions about an unknown mean . Because a second unknown, , is present,

1 Confidence Intervals for Means. 2 When the sample size n< 30 case1-1. the underlying distribution is normal with known variance case1-2. the underlying.

Chapter 7 – Confidence Intervals and Sample Size

Confidence Intervals and Sample Size

Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 8-1 Chapter 8 Confidence Interval Estimation Business Statistics, A First Course.

Confidence Intervals for the Mean (σ Unknown) (Small Samples)

Confidence Intervals Chapter 6. § 6.1 Confidence Intervals for the Mean (Large Samples)

Section 8.2 Estimating  When  is Unknown

SECTION 6.4 Confidence Intervals for Variance and Standard Deviation Larson/Farber 4th ed 1.

Chapter 6 Confidence Intervals.

© 2002 Thomson / South-Western Slide 8-1 Chapter 8 Estimation with Single Samples.

Confidence Intervals Confidence Interval for a Mean

Confidence Intervals Chapter 6. § 6.1 Confidence Intervals for the Mean (Large Samples)

© The McGraw-Hill Companies, Inc., Chapter 6 Estimates and Sample Size with One Sample.

Chapter 6.1 Normal Distributions. Distributions Normal Distribution A normal distribution is a continuous, bell-shaped distribution of a variable. Normal.

Normal Probability Distributions Larson/Farber 4th ed 1.

Unit 7 Section : Confidence Intervals for the Mean (σ is unknown)  When the population standard deviation is unknown and our sample is less than.

CHAPTER SIX Confidence Intervals.

Determination of Sample Size: A Review of Statistical Theory

Confidence Intervals & Sample Size Chapter 7. Introduction One aspect of inferential statistics is estimation, which is the process of estimating the.

© Copyright McGraw-Hill 2000

CHAPTER SIX Confidence Intervals.

Confidence Intervals for the Mean (Small Samples) 1 Larson/Farber 4th ed.

Estimating a Population Mean:  Known

Confidence Intervals for Variance and Standard Deviation.

Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Section 7-4 Estimating a Population Mean:  Not Known.

Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall

CONFIDENCE INTERVALS.

Chapter 7 Confidence Intervals and Sample Size © Copyright McGraw-Hill

Point Estimates point estimate A point estimate is a single number determined from a sample that is used to estimate the corresponding population parameter.

Chapter 5 Normal Probability Distributions 1 Larson/Farber 4th ed.

Aim: What are confidence intervals for means that have unknown standard deviations and sample sizes less than 30? Quiz Friday.

Confidence Interval Estimation of Population Mean, μ, when σ is Unknown Chapter 9 Section 2.

9.2 C ONFIDENCE I NTERVALS About the Population Mean when Population Standard Deviation is Unknown Obj: Use sample data to create a confidence interval.

Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1 Section 6.2 Confidence Intervals for the Mean (  Unknown)

Section 6.2 Confidence Intervals for the Mean (Small Samples) Larson/Farber 4th ed.

Section 6-1 – Confidence Intervals for the Mean (Large Samples) Estimating Population Parameters.

Confidence Intervals. Point Estimate u A specific numerical value estimate of a parameter. u The best point estimate for the population mean is the sample.

SWBAT: -Interpret the t-distribution and use a t- distribution table -Construct a confidence interval when n

Section 6.2 Confidence Intervals for the Mean (Small Samples) © 2012 Pearson Education, Inc. All rights reserved. 1 of 83.

Section 5.1 Introduction to Normal Distributions © 2012 Pearson Education, Inc. All rights reserved. 1 of 104.

Chapter 8 Confidence Intervals Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin.

Confidence Intervals and Sample Size

Confidence Intervals and Sample Size

Confidence intervals for m when s is unknown

Chapter 5 Normal Probability Distributions.

Chapter 6 Confidence Intervals.

Section 6-4 – Confidence Intervals for the Population Variance and Standard Deviation Estimating Population Parameters.

Section 2: Estimating with Small Samples

Confidence Intervals Topics: Essentials Inferential Statistics

Chapter 6 Confidence Intervals.

Normal Probability Distributions

Upcoming Schedule PSU Stat 2014

Confidence Intervals for a Standard Deviation

Upcoming Schedule PSU Stat Jan 2015

Chapter 7 Lecture 3 Section: 7.5.

Elementary Statistics: Picturing The World

Chapter 5 Normal Probability Distributions.

Chapter 6 Confidence Intervals.

Chapter 5 Normal Probability Distributions.

Chapter 7 Lecture 3 Section: 7.5.

Presentation transcript:

7.2 Confidence Intervals When SD is unknown

The value of , when it is not known, must be estimated by using s, the standard deviation of the sample. When s is used, especially when the sample size is small (less than 30), critical values greater than the values for are used in confidence intervals in order to keep the interval at a given level, such as the 95%. These values are taken from the t Distribution

Characteristics of the t Distribution 1. It is bell-shaped. 2. It is symmetric about the mean. 3. The mean, median, and mode are equal to 0 and are located at the center of the distribution. 4. The curve never touches the x axis. 5. The variance is greater than 1. (SD > 1) 6. The t distribution is actually a family of curves based on the concept of degrees of freedom, which is related to sample size. 7. As the sample size increases, the t distribution approaches the standard normal distribution.

Degrees of Freedom (d.f.) The degrees of freedom for a confidence interval for the mean are found by subtracting 1 from the sample size. That is, d.f. = n – 1. Example: If the sample size is 30, the d.f. will be 29.

Formula for a Specific Confidence Interval for the Mean When  is unknown and n < 30 The degrees of freedom are n – 1. We will use the table in the back page of the book to help us with this formula.

Find the t α/2 value for a 95% confidence interval when the sample size is 22. Degrees of freedom are d.f. = 21.

Ten randomly selected people were asked how long they slept at night. The mean time was 7.1 hours, and the standard deviation was 0.78 hours. Find the 95% confidence interval of the mean time. Assume the variable is normally distributed.

Practice: p , 12, 13, 14, 15, 16, 18