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**Estimating a Population Variance**

Section 7.5 Estimating a Population Variance

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

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

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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).

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**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

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**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!

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**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.

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**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)

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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.

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**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

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**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.

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

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1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Chapter 11 Inferences About Population Variances n Inference about a Population Variance n.

1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Chapter 11 Inferences About Population Variances n Inference about a Population Variance n.

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