Presentation on theme: "Estimating a Population Variance"— Presentation transcript:
1Estimating a Population Variance Section 7.5Estimating a Population Variance
2Symbol Check = population mean = population standard deviation = sample standard deviation= sample mean= population variance= sample variance
3Estimators ofThe 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).
4Topic Preview – Sneak Peak Constructing Confidence IntervalsRequirements1.) 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 VarianceConfidence Interval for the Population Standard Deviation????RLRL
5Student t Distribution Chi-square Distribution Our DistributionsNormal DistributionStudent t DistributionChi-square DistributionEstimates of proportions or means with knownEstimates of means with known s.Estimates of variance or standard deviations.NEW!
6Properties of the Chi-square Distribution Uses Table A4To find your Chi-square distribution value you must know:Degrees of Freedom ( df = n-1)Area located to the right of the critical value.
7Properties of the Chi-square Distribution Chi-square is NOT symmetricHowever, the distribution becomes more symmetric as the degrees of freedom increaseInterval Notation: (s²-E < σ <s²+E)Interval Notation: (s²-E, s²+E)Interval Notation: (s²±E)
8Using Table A4Construct a confidence interval for the population standard deviation σ with a confidence level of 95% and a sample size of n=10.
9Constructing 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.404938843859402743184813465740335004482343344317
10Determining Sample Size We want to be 95% confident that our estimate is within 20% of the true value of σ. Find the sample size.