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The Rule of Sample Proportions (RoSP) and how to use it to construct confidence intervals for estimating the true population proportion when the true proportion is unknown. It includes the concept of sampling distribution, the 68-95-99.7 rule, and the process of building a confidence interval around a sample proportion.
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IF: 1. There is a population proportion of interest
Next, suppose we do not know the true population proportion value. This is far more common in reality! How can we use information from the sample to estimate the true population proportion? Suppose we have a sample of 200 students in STAT 100 and find that 28 of them are left handed. Our sample proportion is: 0.
We can now estimate the standard deviation of the sample proportion based on a sample of size 200: Hence, 2 standard deviations = 2×.025 =. On the following two slides, we’ll pretend that the true population proportion is 0.12.
Definition of “95% confidence interval for the true population proportion” : An interval of values computed from the sample that is almost certain (95% certain in this case) to cover the true but unknown population proportion. The plan:
Suppose we want a 90% confidence interval instead of 95%. How many standard deviations span the middle 90% of the normal curve?
Since 90% is in the middle, there is 5% in either end. So find z for .05 and z for .95.