Download presentation

1
**Estimating a Population Variance**

Section 7.5 Estimating a Population Variance

2
**Symbol Check = population mean = population standard deviation**

= sample standard deviation = sample mean = population variance = sample variance

3
Estimators of The sample variance is the best point estimate of the population variance . The sample standard deviation s is commonly used as a point estimate of (even though it is a biased estimate).

4
**Topic Preview – Sneak Peak**

Constructing Confidence Intervals Requirements 1.) The sample is a simple random sample. 2. The population must have a normal distribution (even if sample is large). Confidence Interval for the Population Variance Confidence Interval for the Population Standard Deviation ???? R L R L

5
**Student t Distribution Chi-square Distribution**

Our Distributions Normal Distribution Student t Distribution Chi-square Distribution Estimates of proportions or means with known Estimates of means with known s. Estimates of variance or standard deviations. NEW!

6
**Properties of the Chi-square Distribution**

Uses Table A4 To find your Chi-square distribution value you must know: Degrees of Freedom ( df = n-1) Area located to the right of the critical value.

7
**Properties of the Chi-square Distribution**

Chi-square is NOT symmetric However, the distribution becomes more symmetric as the degrees of freedom increase Interval Notation: (s²-E < σ <s²+E) Interval Notation: (s²-E, s²+E) Interval Notation: (s²±E)

8
Using Table A4 Construct a confidence interval for the population standard deviation σ with a confidence level of 95% and a sample size of n=10.

9
**Constructing a Confidence Interval**

Twelve different video games showing substance use were observed and the duration of times of game play (in seconds) are listed below. Use the sample data to construct a 99% confidence interval estimate of σ, the variance and standard deviation of the duration of game play. 4049 3884 3859 4027 4318 4813 4657 4033 5004 4823 4334 4317

10
**Determining Sample Size**

We want to be 95% confident that our estimate is within 20% of the true value of σ. Find the sample size.

11
Homework Pg #2, 6, 7, 16, 19

Similar presentations

OK

Confidence Intervals for Variance and Standard Deviation.

Confidence Intervals for Variance and Standard Deviation.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on france in french Ppt on regulated power supply Ppt on evolution and classification of computers Ppt on application of linear algebra in computer graphics Ppt on cloud computing services Download ppt on live line maintenance usa Ppt on national education policy 1986 super Ppt on principles of object-oriented programming advantages Ppt on central bank of india Ppt on digital advertising