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# lect14 - Game III Review Sampling Distribution of Sample...

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Game III Review Sampling Distribution of Sample Mean Outline Game III Review Sampling Distribution of Sample Mean Sampling Distribution of Sample Proportion Ranges for parameters Conﬁdence Interval for the Proportion 1 / 15 ISOM 2500 Lect 14: Sampling Distribution; CI for p

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Game III Review Sampling Distribution of Sample Mean Game III Review Purpose: ﬁnd out the proportion of M&M candies of colors blue, orange, and red in the class We used the sample proportion ˆ p to estimate the population proportion p . Sample proportion is a special case of sample mean ¯ x : In Game III, for the i th candy in the bag, assign x i = 1 if it’s blue, orange or red, assign x i = 0 otherwise. Then we have that the sample proportion ˆ p = x 1 + x 2 + ··· + x n n = ¯ x Similarly, population proportion p is a special case of population mean μ . 2 / 15 ISOM 2500 Lect 14: Sampling Distribution; CI for p
Game III Review Sampling Distribution of Sample Mean Sampling Distribution of Sample Proportion Sample Estimates of Population Parameters The sample statistics ¯ x , ˆ p , s 2 and s are commonly used to estimate the population parameters μ , p , σ 2 and σ . As we have seen in Game III, the sample estimates do not match the population parameters, and vary from sample to sample. Once we admit that we might have gotten a different value if we had gotten a different sample, we need to describe how different the result might have been. 3 / 15 ISOM 2500 Lect 14: Sampling Distribution; CI for p

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Game III Review Sampling Distribution of Sample Mean Sampling Distribution of Sample Proportion Sampling Distribution To quantify this sample-to-sample variation , we introduce a new population: The population of values of the sample statistic – the set of all possible values of the sample statistic, one for each possible sample (of a particular size n ) that could be drawn from the original population. The distribution of the population of sample statistic values is called the sampling distribution of the statistic . Example, for Game III, What is the population of sample statistic values (proportions)? How do the sample proportions in class relate to the population of sample proportions?
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lect14 - Game III Review Sampling Distribution of Sample...

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