Presentation on theme: "Section 7.5 Estimating a Population Variance. Symbol Check = population standard deviation = sample standard deviation = population mean = sample mean."— Presentation transcript:
Section 7.5 Estimating a Population Variance
Symbol Check = population standard deviation = sample standard deviation = population mean = sample mean = population variance = sample variance
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).
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 RL ???? RL
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!
Properties of the Chi-square Distribution 1.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.
Properties of the Chi-square Distribution 2.Chi-square is NOT symmetric ▫However, the distribution becomes more symmetric as the degrees of freedom increase Interval Notation: (s²-E < σ
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.
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
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.