STA215H5 Lecture Notes - Lecture 16: Simple Random Sample, Bernoulli Distribution, Confidence Interval
STA215; Chapter 16 - Confidence Intervals
Confidence interval: range of values dened that there is a specied probability that the value of
a parameter lies within it
● EX: PEPSI COKE
○Pepsi-Cola Co. is interested in determining the proportion of UTM students who
favor Pepsi over Coke. A random sample of 100 students shows that 40 students
favor Pepsi over Coke. Use this information to construct a 95% condence
interval for the proportion of all students in this market who prefer Peps
Bernoulli Distribution
●
INTERVAL ESTIMATE OF P
● Draw a simple random sample of size n from a population with unknown proportion p of
successes. An (approximate) condence interval for p is:
● where z∗ is a number coming from the Standard Normal distribution (in the z-table) that
depends on the condence level required
● EX: YES REPONSES
○A simple random sample of 400 individuals provides 100 ’Yes’ responses.
○a) What is the point estimate of the proportion of the population that would
provide ’Yes’ responses?
■phat = 100/400
■ = ¼
○b) What is the point estimate of the standard error of the proportion, σˆ p?
Document Summary
Confidence interval: range of values de ned that there is a speci ed probability that the value of a parameter lies within it. Pepsi-cola co. is interested in determining the proportion of utm students who favor pepsi over coke. A random sample of 100 students shows that 40 students favor pepsi over coke. Use this information to construct a 95% con dence interval for the proportion of all students in this market who prefer peps. Draw a simple random sample of size n from a population with unknown proportion p of successes. Where z is a number coming from the standard normal distribution (in the z-table) that depends on the con dence level required. A simple random sample of 400 individuals provides 100 "yes" responses. C) compute the 95% con dence interval for the population proportion. Just look for one value, the other value will just be the opposite sign of it.