sLecture7dPBS - Lecture #7 Learning Objectives 1. Be able...

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Lecture #7 Learning Objectives 1. Be able to compute the point and interval estimate for a population proportion using the Normal approximation to the Binomial. 2. Be able to determine the size of a simple random sample necessary to estimate a population proportion with a specified level of precision. 3. Be able to conduct hypothesis tests about a population proportion using the Normal approximation Normal approximation to the Binomial. 4. Be able to compute the point and interval estimate for the difference between two population proportions using the Normal approximation to the Binomial. 5. Be able to conduct statistical tests about the difference between the proportions of two populations using the Normal approximation to the Binomial. 6. Know the definition of the following terms: P r o p o r t i o n Difference between Two Proportions Pooled Proportion Normal Approximation to the Binomial Wilson Estimate “Learning without thought is labor lost; thought without learning is perilous.” – Confucius (551 BC – 479BC)
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BM330 - Lecture 7 Inference About a Population Proportion We have focused our attention up to this point on variables “measured” on an interval or ratio scale, e.g., income in $, diameter in inches, time in minutes. We now turn our attention to nominal or categorical variables, e.g., gender. In particular, we are interested in the proportion of items or subjects that are in a particular category. We might like to know the proportion of voters planning to vote in favor of a candidate in an upcoming election. We might like to know what proportion of consumers prefer ibuprofen to aspirin. Definition: A population proportion, p , is the fraction of a population that possesses a given characteristic. It is the probability of randomly selecting an item that possesses the characteristic from the population. If a population is comprised of 60 males and 40 females, the population proportion, p , for females is 0.40. We have 40 chances in 100 of randomly selecting a female. Parameter: N X p = = 100 40 Definition: A sample proportion is the fraction of a sample that possesses a given characteristic. If we randomly sample 10 subjects from the population with 60 males and 40 females, and observe 5 females, the sample proportion is 0.50. Point Estimate: trials of successes of n x p # # 10 5 ˆ = = = 1
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BM330 - Lecture 7 The Sampling Distribution of trials of successes of n X p # # ˆ = = : Recall that X, # of success in n trials of an experiment, has a Binomial distribution if the n trials are independent and identical, and the probability of success (proportion), p , remains constant for the experiment. If the n trials represent a random sample, then X is a sample statistic, and its sampling distribution is the Binomial. Example
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sLecture7dPBS - Lecture #7 Learning Objectives 1. Be able...

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