confidence intervals with proportions using the calculator notes: page 166
TRANSCRIPT
Confidence Intervals with Proportions
Using the Calculator
Notes: Page 166
A May 2000 Gallup Poll found that 38% of a random sample of 1012 adults said that they believe in ghosts. Find a 95% confidence interval for the true proportion of adults who believe in ghost.
Assumptions:
•Have an SRS of adults
•np =1012(.38) = 384.56 & n(1-p) = 1012(.62) = 627.44 Since both are greater than 10, the distribution can be approximated by a normal curve
•Population of adults is at least 10,120.
We are 95% confident that the true proportion of adults who believe in ghosts is between 35% and 41%.
Step 1: check assumptions!
Step 2: make calculations
Step 3: conclusion in context
Assumptions:
•Have an SRS of adults
•np =1012(.38) = 384.56 & n(1-p) = 1012(.62) = 627.44 Since both are greater than 10, the distribution can be approximated by a normal curve
•Population of adults is at least 10,120.
We are 95% confident that the true proportion of adults who believe in ghosts is between 35% and 41%.
Step 1: check assumptions!
Step 2: make calculations
Step 3: conclusion in context
Calculator: STAT, TESTS, 1-Prop Z Intervalx=(n)(p), always round up = 385n=1012C-Level = .95= (.35, .41)
The manager of the dairy section of a large supermarket took a random sample of 250 egg cartons and found that 40 cartons had at least one broken egg. Find a 90% confidence interval for
the true proportion of egg cartons with at least one broken egg.
Assumptions:
•Have an SRS of egg cartons
•np =250(.16) = 40 & n(1-p) = 250(.84) = 210 Since both are greater than 10, the distribution can be approximated by a normal curve
•Population of cartons is at least 2500.
198,.122.250
)84(.16.645.116.
We are 90% confident that the true proportion of egg cartons with at least one broken egg is between 12.2% and 19.8%.
Step 1: check assumptions!
Step 2: make calculations
Step 3: conclusion in context
Assumptions:
•Have an SRS of egg cartons
•np =250(.16) = 40 & n(1-p) = 250(.84) = 210 Since both are greater than 10, the distribution can be approximated by a normal curve
•Population of cartons is at least 2500.
We are 90% confident that the true proportion of egg cartons with at least one broken egg is between 12.2% and 19.8%.
Step 1: check assumptions!
Step 2: make calculations
Step 3: conclusion in context
Calculator: STAT, TESTS, 1-Prop Z Intervalx=(n)(p), always round up = 40n=250C-Level = .90= (.122, .198)
Another Gallop Poll is taken in order to measure the proportion of adults who approve of attempts to clone humans. What sample size is necessary to be within + 0.04 of the true proportion of adults who approve of attempts to clone humans with a 95% Confidence Interval?
To find sample size:
However, since we have not yet taken a sample, we do not know a p-hat (or p) to use!
npp
zm1
*
What p-hat (p) do you use when trying to find the sample size for a given margin of error?
.1(.9) = .09
.2(.8) = .16
.3(.7) = .21
.4(.6) = .24
.5(.5) = .25
By using .5 for p-hat, we are using the worst-case scenario and using the largest SD in our calculations.
Remember that, in a binomial distribution, the histogram with the
largest standard deviation was the one for probability of success of 0.5.
Another Gallop Poll is taken in order to measure the proportion of adults who approve of attempts to clone humans. What sample size is necessary to be within + 0.04 of the true proportion of adults who approve of attempts to clone humans with a 95% Confidence Interval?
60125.600
25.96.104.
5.5.96.104.
5.5.96.104.
1*
2
n
n
n
n
npp
zm
Use p-hat = .5
Divide by 1.96
Square both sides
Round up on sample size
Homework:
Page 167 and 168, add calculator work to each problem. (Due Monday)