inference for a population proportion section 12.1 ap registration deadline: march 17 th late fee...
TRANSCRIPT
![Page 1: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/1.jpg)
Inference for a Population ProportionSection 12.1
AP Registration Deadline:March 17th
Late Fee ($50):March 18th – 24th
Financial Aid Application Due: March 1st
![Page 2: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/2.jpg)
Remember Conditions for Inference
Data are an SRS from the population of interest.
Observations are independent (pop. ≥ 10*n)
Sampling Distribution is approx. normal Today, we’re dealing with proportions, so np ≥ 10 and n(1- p) ≥ 10.
![Page 3: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/3.jpg)
Standard Error Replace standard deviation by the standard
error of (or standard deviation of )
To get a confidence interval of the form
Estimate ± z* SE
![Page 4: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/4.jpg)
Inference for a Population Proportion
Draw an SRS of size n from a large population with unknown proportion p of successes. An approximate level C confidence interval for p is
where z* is the upper (1 – C)/2 standard normal critical value.
![Page 5: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/5.jpg)
Remember: State Plan Do Conclude
Statistics Problems Demand Consistency!!!
![Page 6: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/6.jpg)
Example 1A Gallup Poll found that 28% of a SRS of 682 American adults expect to inherit money. Construct a 90% Confidence interval for the true proportion.
State: know what parameters we’re estimating & at what confidence level
We want to estimate p = the true proportion of US adults who expect to inherit $ with 90% confidence.
![Page 7: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/7.jpg)
Example 1Plan: choose method & check conditions
Method: Proportions
Conditions:Random:
Independent:
Normal:
Assume Gallup used correct sampling procedures
n = 682, the population of adults is much larger than 6820 (pop. ≥ 10*n), so assume independence.
sampling distribution of is approx. normal
![Page 8: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/8.jpg)
Example 1Do: if conditions are met, perform calculations
.
![Page 9: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/9.jpg)
Example 1Conclude: interpret the interval in the context of the problem
We are 90% confident that the true percentage is between 25.17% and 30.83%.
![Page 10: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/10.jpg)
YOUR TURN!!!The New York Times and CBS News conducted a nationwide poll of 1048 randomly selected 13- to 17-year-olds. Of these teenagers, 692 had a television in their room. We will act as if the sample were an SRS.
Construct a 95% confidence interval for the proportion of all people in this age group who have a TV in their room.
![Page 11: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/11.jpg)
!!!!We are trying to estimate the population proportion of teenagers who have a TV in their room at a 95% confidence level.
Method: proportions, Conditions: SRS: Yes!
Independent: Population of teenagers ≥ 10*1048 Yes! Normal: (1048)(.66) ≈ 692 ≥ 10 and (1048)(.34) ≈ 356 ≥ 10
Yes!
We are 95% confident that the true population proportion of teenagers with a TV in their room falls between .63 and .69.
![Page 12: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/12.jpg)
Choosing the sample size
Since the margin of error contains the sample proportion, we need to guess this value when choosing n.
We will call this guess p*.
![Page 13: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/13.jpg)
Choosing the sample sizeTwo ways to get p*:
1. Use p* based on a past experience with similar studies. Cover several calculations to cover the range of -values you might find.
Better to use when you have done a similar study.
2. Use p* = 0.5 as the guess. The margin of error m is largest when . Use when you suspect to be between 0.3 and 0.7
![Page 14: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/14.jpg)
Choosing the sample sizeSo…
Where p* is a guessed value for the sample proportion.
![Page 15: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/15.jpg)
Example 12.9, p. 696 Gloria Chavez and Ronald Flynn are the
candidates for mayor in a large city. You are planning a sample survey to determine what percent of the voters plan to vote for Chavez. This is a population proportion p. You will contact an SRS of registered voters in the city. You want to estimate p with 95% confidence and a margin of error no greater than 3%, or 0.03. How large a sample do you need?
![Page 16: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/16.jpg)
Example 12.9, p. 696Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. You are planning a sample survey to determine what percent of the voters plan to vote for Chavez. This is a population proportion p. You will contact an SRS of registered voters in the city. You want to estimate p with 95% confidence and a margin of error no greater than 3%, or 0.03. How large a sample do you need?
Should we use p* = 0.5? YES!
![Page 17: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/17.jpg)
Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. You are planning a sample survey to determine what percent of the voters plan to vote for Chavez. This is a population proportion p. You will contact an SRS of registered voters in the city. You want to estimate p with 95% confidence and a margin of error no greater than 3%, or 0.03. How large a sample do you need?
So we want:
32.66 ≤
1067.1≤ n
So we need n = 1068 to satisfy this inequality.
![Page 18: Inference for a Population Proportion Section 12.1 AP Registration Deadline: March 17 th Late Fee ($50): March 18 th – 24 th Financial Aid Application](https://reader030.vdocuments.mx/reader030/viewer/2022032723/56649d0b5503460f949dee4d/html5/thumbnails/18.jpg)
Homework: p. 694: 12.8, 12.9 P. 696: 12. 10, 12.11
Due: Tuesday