Section 1: Estimating with large samples Chapter 8: Estimation Section 1: Estimating with large samples

statistical inference – analyzing, interpreting, and forming conclusions about data estimation – involves approximating the value of an unknown parameter hypothesis testing – involves choosing between two opposing statements (hypotheses) concerning a population

Point estimate the value of a statistic that estimates the value of the parameter the sample mean, x, is the point estimate of the population mean, the sample standard deviation, s, is the point estimate of the population standard deviation, σ

Confidence interval estimate consists of an interval of numbers, along with the likelihood that the interval contains the unknown parameter (confidence level) confidence levels measure the reliability of an estimate c – confidence level (0.90, 0.95, 0.99) zc – critical values for a confidence level of c; z values corresponding to c

Levels of Confidence and Corresponding Critical Values Confidence Level Critical Value zc 70% 1.04 75% 1.15 80% 1.28 85% 1.44 90% 1.645 95% 1.96 98% 2.33 99% 2.58

Formula for Confidence Interval for

Example A sample of 41 male runners age 35 – 59 years showed a sample mean systolic blood pressure of 123 and standard deviation 17. Find the interval that contains the mean systolic blood pressure of all male runners age 35 – 59 with a 95% confidence level.

Example Walter jogs 3 miles and has recorded his times to run the 3 miles. For the 90 times he recorded, his mean time is 22.50 minutes with a standard deviation of 2.40 minutes. Find a 99% confidence interval.