Estimating Population Parameters Mean Variance and standard deviation

Estimating Population Parameters ü Mean ü Variance (and standard deviation) • Proportion

Population Proportion • What percent of a population has some characteristic? • The characteristic is binary (two values) – Male or female – Defective or operable – For or against some issue • The variable p represents the percent of the sample that has the characteristic – q is the percent that has the other characteristic – p+q=1

Point estimate • The proportion for the sample is a good enough point estimate for the proportion of the population. • However, we also want a confidence interval for the estimate, which means we need a margin of error – We need p, sample size, and degree of confidence (z or t)

For example • How many of us have seen the move “Wedding Crashers” ? • Samples = • Degree of confidence = • t= • p= • E= • Confidence interval = ( )

Live example • Assume we asked 40 people at lunch, 55% said they have seen the move • Samples = • Degree of confidence = • z= • p= • E= • Confidence interval = ( )

Your Turn • • We polled 45 upperclassmen and 16 underclassmen 65% of the upperclassmen drink coffee 27% of the underclassmen do Find a interval estimate for the population of upperclassmen and underclassmen who drink coffee

Determining Sample Size • How many people should we ask to get the margin of error and degree of confidence we want? – We need p – We need to choose E and the degree of confidence • What if we don’t know p? – Use 0. 25 for pq

For example • What proportion of seniors have their own car? • E= • Degree of confidence = • z= • pq =

Live Example • 60% of all Monmouth University students receive financial aid • We want to study financial aid given to Middletown students. • How many samples should we take? • E= • Degree of confidence = • z= • pq =

Your turn • Our sample of 35 people, 13 are left-handed – What is the point estimate of the proportion of left-handed people in the class? – What is the confidence interval (90% degree of confidence) – What if we want to reduce our margin of error in half, how many samples do we need?

Homework • 1. 2. 3. 4. • 5. 6. 7. Find the interval estimate for the following samples: p = 0. 3, n = 45, 95% confidence p = 0. 81, n = 19, 90% confidence p = 0. 5, n = 94, 99% confidence p = 0. 08, n = 31, 95% confidence Find the number of samples p = 0. 4, E = 1%, 90% confidence p = 0. 95, E = 3%, 95% confidence p = unknown, E = 5%, 99% confidence

More homework 8. A poll of NJ high school seniors shows 28 applied to Rutgers, 18 did not. Find an interval estimate for the percent of the population that applied to RU. 9. In poll of 20 PT Cruiser owners, 70% said they would buy another model of the car again. Find an interval estimate for the percent of the population that would but the car a second time. 10. A sample of i. Phones showed one was defective and 25 operational. Find an interval estimate for the percent of the population that is defective.

Still More Homework 11. Last year, 70% of seniors went to the prom. If we poll this year’s class on their prom plans, how many samples do we need to get a 3% margin of error? Assume a 99% degree of confidence. 12. We want to estimate the results of the school board election. How many samples do we need if the a margin of error is 2%? Assume a 95% degree of confidence. 13. Four out of five dentist recommend our toothpaste. To verify this claim, how many samples do we need if we want a 4% margin of error. Assume a 90% degree of confidence.

Answers 1. 2. 3. 4. 5. 6. 7. (0. 17, 0. 43) (0. 65, 0. 97) (0. 37, 0. 63) (-0. 02, 0. 18) n = 6495 n = 202 n = 663 8. Do. C = 95%, (0. 47, 0. 75) – – Do. C = 90%, (0. 49, 0. 73) Doc = 99%, (042, 0. 80) 9. Do. C = 95%, (0. 49, 0. 91) 10. Do. C = 95%, (-0. 04, 0. 12) 11. n = 1547 12. n = 2401 13. n = 271