READING HANDOUT #5 PERCENTS

Container of Beads Container has 4,000 beads 20% - RED 80% - WHITE Sample of 50 beads with pallet. Population - the 4,000 beads in container Sample - the 50 beads selected Variable - color of bead Parameter - % RED beads in Box (20%) Statistic - % RED beads in sample

Terminology:

n Note: sample % is an estimate of the population % n i.e. p x 100% is an estimate of p x 100%

Facts about Sampling Distribution of Sample % EV(sample %) = p x 100% SE(sample %) = p x (1-p) x 100% n For n reasonably large, the distribution of the sample % is approximately normal (Central Limit Theorem)

In general, increasing the number of draws (sample size)... n No change in EV(%) n Decreases SE(%) (sample AVG was similar)

Finding Chances about sample % Use Z-score as with averages, i.e.

Practical Situation --- we will not know the population % --- in order to estimate the pop. % we take sample and find sample %

Confidence Intervals about Population % n Because of normality of sample %, we are 95% certain that the sample % is within 2 SE(sample%)’s of the population %. n As with the AVG, we must “approximate” the SE(sample %) l Why? l We don’t know p in SE formula

EV and SE Formulas for Sample % EV(sample %) = p x 100% SE(sample %) = p x (1-p) x 100% n

Confidence Intervals about Population % n Because of normality of sample %, we are 95% certain that the sample % is within 2 SE(sample%)’s of the population %. n As with the AVG, we must “approximate” the SE(sample %) l Why? l We don’t know p in SE formula l Use p instead

Approximate SE for Sample % SE(sample %) = p x (1-p) x 100% n

Confidence Intervals

Margin of Error n Reporting of Survey Results “22% of those sampled favored … and there was a margin of error of 3%” n margin of error = 2SE(sample %), (i.e. the “ “ used for 95% CI)