Chapter 9 %28pages 118-138%29

Chapter 9 %28pages 118-138%29 - MSIT 3000 Chapter 9 Section...

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MSIT 3000 Chapter 9 Section 9.1: Simulations To learn more about the variability, we have to imagine . We probably will never know the value of the true proportion of an event in the population. But it is important to us, so we’ll give it a label, p for “true proportion.” A simulation is when we use a computer to pretend to draw random samples from some population of values over and over. A simulation can help us understand how sample proportions, ‘s, vary due to random sampling. Even though the ’s vary from sample to sample, they do so in a pattern that we can model and understand. So let’s do a simulation using a binomial situation and see what happens. 118 ˆ p ˆ p
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Roll your die five times and record the value on each roll. Let a success be a 1 or 2. So P(Success) = 1/3. Find the proportion of successes in your five rolls. Report your sample statistic, , to the class. I’ll create a dotplot where each dot represents one statistic from one sample. ____________________________________ 0 0.2 0.4 0.6 0.8 1.0 119 ˆ p ˆ p
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MSIT 3000 Section 9.2: Sampling Distribution for Proportions Here’s a histogram of the counts for 500 experiments where each experiment is rolling 5 dice. Each mark on the histogram represents the number of successes from tosses of five dice: The shape of the distribution is unimodal and approximately symmetric, aka approximately Normal! 120
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The distribution of proportions over many independent samples from the same population is called the sampling distribution of the proportions. For distributions that are bell-shaped and centered at the true proportion, p , we can use the sample size n to find the standard deviation of the sampling distribution (aka standard error): The particular Normal model, is a sampling distribution model for the sample proportion . It won’t work for all situations, but it works for most situations that you’ll encounter in practice. Since it doesn't always work, we'll look at how to determine when we can use the Normal model for situations with proportions. 121 (1 ) ˆ ( ) p p pq SD p n n - = = ˆ , pq p N p n ÷ :
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MSIT 3000 Section 9.3: Assumptions and Conditions Independence Assumption : The sampled values must be independent of each other. Randomization Condition : If your data come from an experiment, subjects should have been randomly assigned to treatments. If you have a survey, your sample should be a simple random sample of the population, or some other unbiased sampling method. 10% Condition : If sampling has not been made with replacement, then the sample size, n , must be no larger than 10% of the population. Sample Size Assumption : The sample size, n , must be large enough. Success/Failure Condition
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Chapter 9 %28pages 118-138%29 - MSIT 3000 Chapter 9 Section...

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