DobbinChapter8RevisedJan32010

DobbinChapter8RevisedJan32010 - Chapter 8 PROPORTIONS Many...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 8 PROPORTIONS Many statistical studies produce counts rather than measurements. Example: Did you vote in the last election? The response would be either a Yes or a No. If I did a survey, I would accumulate the count of Yes responses and describe this count as a proportion of the total. Proportion that voted = = 338/ 1500= .225 Example: What academic year are you in at Purdue. The response would be either Freshman, Sophomore, Junior, or Senior. Again, I could accumulate the count of each and describe each as a proportion of the total. Proportion of freshmen = .2045 Proportion of sophomores = .2688 Proportion of juniors = .3215 Proportion of seniors = .2052 Population and Sample proportions: In statistical sampling we often want to estimate the proportion, p, of successes in a population. Success is when the categorical variable takes on one particular value of interest. p = count of successes in population size of population = X / N = a fixed but unknown value between 0 and 1.0 When we take a sample of our population ; our estimator is the sample proportion of successes: p = count of successes in sample size of sample Page 1 = X / n = a known value but another sample would give a different value. Example: 1. You flip a coin 20 times and record whether a head (success) or a tail is tossed. In this sample, a head is recorded 11 times. What is the sample proportion of heads? = 11/20 = .55 Inference for a Single Proportion: So far we have only looked at making a statistical inference on population means. Now we will look at making a statistical inference on a population proportion. Examples: A newspaper runs a poll to determine the popularity of a congressman in the district. The poll results in a value = .52. In this example we are interested in estimating the unknown proportion p in the population of all voters in the district. The point estimate of that population parameter p is the sample proportion p , a statistic. Sampling Distribution of a Sample Proportion: If you select a SRS of size n from a large population, and determine the sample proportion in favor of a certain issue, p = X/ n, you will find that: The sample proportion is a statistic and fluctuates, The sampling distribution of p is approximately normal provided the sample size is big enough to produce at least 15 success and 15 failures, and does not exceed 1% of the population....
View Full Document

Page1 / 12

DobbinChapter8RevisedJan32010 - Chapter 8 PROPORTIONS Many...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online