Unit 8: Estimating with Confidence Estimating a population proportion p

#12 59% of people in the sample said “Yes” “For results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is +-3% points” Margin of error meaning State and interpret the 95% confidence interval Interpret the confidence level If we repeat the sampling procedure many times, the sample proportion would be within 3% pts of the true proportion in 95% of the samples (0.56, 0.62) We are 95% confident that the interval from 0.56 to 0.62 captures the true proportion of those who would like to lose weight. If we were to repeat the sampling procedure many times, about 95% of the confidence intervals computed would contain the true proportion of those who would like to lose weight.

State & explain the three conditions (RIN) Objectives: State & explain the three conditions (RIN) Construct and interpret a ConfInt for a pop. proportion Determine critical values for a ConfInt using a table Emphasize the appearance of “and confidence interval” b\c there is a huge difference between the two parts of this objective. Let students know that the conditions required to use a ConfInt should be familiar.

pt.est. is midpt. of interval Recap: pt.est. is midpt. of interval The dist. from pt.est. to either end of the interval is the margin of error IF we created EVERY interval poss. then __C__% of the intervals would contain pop. parameter Give examples of intervals and have students identify the pt. est. and the ME. The blank in bullet 3 is predetermined when we declare how confident we wish to be….

Suppose a SRS of 358 beads results in 135 red beads. Using sample results to estimate p Suppose a SRS of 358 beads results in 135 red beads. This is a point estimate for p

In order to estimate p (the population proportion of red beads) using a confidence interval we must meet the following conditions:

Random

Independent When the population is infinite or we sample with replacement we meet the independence condition. Not likely.

Independent—realistically  If 10n < Pop we meet the independence condition so the standard deviation of the sampling distribution of is

Normal

Definition: When the standard deviation of a statistic is estimated from data, the result is called the standard error of the statistic.

You will need your formula sheet Let’s get back to beads….. You will need your formula sheet