Confidence intervals and population proportions THE FORMULA FOR

Confidence intervals and population proportions

THE FORMULA FOR A CONFIDENCE INTERVAL

ROUNDING ERROR • Because we will be using large numbers, we will have to store the results in the calculator until we get the final answer • We will either have to use the (1) stats (2) test (3) 1 -Prop. ZInt program • Embed the answer in our calculations • Store temporary answers in a memory location for recall

A SIMPLE EXAMPLE—FLU SHOTS…DOES IT HELP? 800 students were selected from a population of 20, 000 and given a flue shot. They were then exposed to the influenza virus and 600 did not get ill. Find a 95% confidence interval of the number of students who would be expected to remain healthy during the flu season.

CRUNCH THE NUMBERS

HOW DO WE FIND THE ZSCORES • Remember our normal distribution is a bell-shaped curve, centered in the middle. • We take half of the remaining curve we want to find the score for • (1) 2 nd Distr. Vars (2) inv. Norm (3) type in our value and apply the appropriate sign.

FIND THE VALUE FOR A 68% (1 SD) CONFIDENCE INTERVAL • 1 -. 68 or 32% of the curve is out side our area • Divide by 2 or we will be using an area of +16% • 2 nd distrvars, invnorm(. 16) = and apply the appropriate sign • So for 68% of our values, we would have a z -score of. 994458 or approximately 1 standard deviation unit from the mean

ONE MORE. . FIND THE ZSCORE FOR 90% OF OUR VALUES 1 -. 9 = 10% Half of 10% is. 05 2 nd distrvars. ; invnorm(. 05), = 1. 645

LARGE NUMBERS—EMBEDDED THE MATH P 15, PG 456

NOW USE THE SOFTWARE (1) Stats (2) test (3) 1 -Prop. ZInt (2) X: 4781; n: 100000; C-level: 95 calculate (3) (. 0465, . 0491)