{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter20

# The Basic Practice of Statistics (Paper) & Student CD

This preview shows pages 1–8. Sign up to view the full content.

Inference about a population proportion BPS chapter 20 © 2006 W.H. Freeman and Company

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Objectives (BPS chapter 20) Inference for a population proportion The sample proportion The sampling distribution of Large sample confidence interval for p Accurate confidence intervals for p Choosing the sample size Significance tests for a proportion p ˆ p ˆ
The two types of data — reminder Quantitative Something that can be counted or measured and then added, subtracted, averaged, etc., across individuals in the population. Example: How tall you are, your age, your blood cholesterol level Categorical Something that falls into one of several categories. What can be counted is the proportion of individuals in each category. Example: Your blood type ( A, B, AB, O ), your hair color, your family health history for genetic diseases, whether you will develop lung cancer How do you figure it out? Ask: What are the n individuals/units in the sample (of size “ n ”)? What’s being recorded about those n individuals/units? Is that a number ( quantitative) or a statement ( categorical)?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
We choose 50 people in an undergrad class, and find that 10 of them are Hispanic: = (10)/(50) = 0.2 (proportion of Hispanics in sample) You treat a group of 120 Herpes patients given a new drug; 30 get better: = (30)/(120) = 0.25 (proportion of patients improving in sample) The sample proportion We now study categorical data and draw inference on the proportion, or percentage, of the population with a specific characteristic. If we call a given categorical characteristic in the population “success,” then the sample proportion of successes, ,is: sample in the ns observatio of count sample in the successes of count ˆ = p ˆ p ˆ p ˆ p ˆ p
Sampling distribution of The sampling distribution of is never exactly normal. But as the sample size increases, the sampling distribution of becomes approximately normal. p ˆ ˆ p p ˆ

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The mean and standard deviation (width) of the sampling distribution are both completely determined by p and n . Thus, we have only one population parameter to estimate, p . Implication for estimating proportions N p , p (1 " p ) n ( ) Therefore, inference for proportions can rely directly on the normal distribution (unlike inference for means, which requires the use of a t distribution with a specific degree of freedom) .
Conditions for inference on p Assumptions: 1. We regard our data as a simple random sample (SRS) from the population. That is, as usual, the most important condition.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern