Statistical Reasoning for everyday life Intro to Probability and Statistics Mr. Spering – Room 113

8.2 Estimating Population Means CONFIDENCE INTERVAL→ Range of values that is likely to contain the value of the population mean. Written as a compound inequality. { low < μ < high } MARGIN OF ERROR→ Range of values likely to contain the population parameter. ???HOW CONFIDENT ARE YOU???

8.2 Estimating Population Means For the purpose of Intro to Probability and Statistics we will use a 95% CONFIDENCE INTERVAL TO ESTIMATE THE POPULATION MEAN → Using the margin of error and the sample mean. The process is as follows. RECALL: NOTATION AND SYMBOL REVIEW: n…Sample size μ…Population mean sx…Sample standard deviation …Sample mean 1.96??

8.2 Estimating Population Means EXAMPLE: A study conducted by the Garbage Project at the University of Arizona involved a sample of 62 households; the households ranged in size from 2 to 11 members. The mean for the sample was 27.4 pounds of garbage per household per week and the standard deviation was 12.5 pounds. What is the population and estimate the population mean. What conclusions can we make? Therefore, the population of Arizona which is an appropriate cluster sample for the USA uses with 95% confidence between 24.2 and 30.6 pounds of garbage per household per week.

8.2 Estimating Population Means How do we choose the correct sample size? WE CHOOSE OUR SAMPLE SIZE DEPENDENT ON MARGIN OF ERROR In other words, normally we know what our acceptable margin of error should be, thus using a little bit of algebra we will choose the correct sample size.

8.2 Estimating Population Means How do we choose the correct sample size? EXAMPLE

8.2 Estimating Population Means Class work: pg 353 # 1-25 all ? 95 Confident