A heart fills with loving kindness is a likeable person indeed.

1. A heart fills with loving kindness is a likeable person indeed.

2. Estimating Proportions and Means Sample estimates Confidence intervals Approximate confidence intervals for p and m

3. Review • Unit: a person or object to be measured • Population: collection of units about which we want information • Sample: collection of units we will measure • Sample size: the number of units in a sample • p: population proportion • : sample proportion

4. Fundamental Rule for Using Data for Inference • The available data can be used to make inferences about a much larger group if the data can be considered to be representativewith regard to the questions of interest.

5. Estimation • Sample estimate of a numerical summary of population (a parameter) is the same numerical summary of sample (a statistic) Eg. Sample estimate of population proportion p is sample proportion • Margin of error for k%: the difference between sample estimate and the parameter is less than margin of error for k% about k% of time.

6. Estimation • A k% confidence interval (C.I.) for a parameter is an interval of values computed from sample data that includes the parameter k% of time: Sample estimate + margin of error for k%

7. p

8. Approximate C.I. for p When are both at least 10: • Margin of error for k% is about where z* is the z score from the standard normal probability table corresponding to (1/2+k/2%).

9. Approximate C.I. for p • An approximate k% C.I. for p is • An approximate 95% C.I. for p is

10. Approximate C.I. for m When • Either the population follows normal curve • Or the sample size n > 30 • The margin of error for k% is about where t* is the t score from the t probability table corresponding to k% and (n-1) df.

11. Approximate C.I. for m • An approximate k% C.I. for m is