Cracking the AP Statistics Exam, 2014 Edition by Princeton Review

Author:Princeton Review [Review, The Princeton]
Language: eng
Format: epub
ISBN: 978-0-8041-2430-0
Publisher: Random House Information Group
Published: 2013-10-14T16:00:00+00:00

For example, to estimate the difference in the proportion of women graduating with a degree in engineering at two major universities in Alabama, we could use the difference in those proportions computed from randomly selected samples of engineering students from each of these universities.

SAMPLING DISTRIBUTION OF A STATISTIC

As seen from these examples, the point estimate statistic is a function of random variables. Therefore, it is a random variable itself. Different samples will result in different estimates. How close or how far can these estimates be from the true value? We can answer this question by studying the distribution of the estimates. The sampling distribution of a statistic is the distribution of estimates (values taken by the statistic) from all possible samples of the same size from the same population.

Example 1: Suppose a student is interested in estimating p, the probability of getting heads when a penny is tossed. Suppose she tosses a penny 50 times and gets 24 heads. This sample of 50 tosses gives her an estimated probability () of = 0.48. So the student decides to see what happens if she repeats the experiment. The histogram and the table on the next page summarize the results of 100 such experiments, each of 50 tosses:

Table 1: Distribution of P(Heads) estimated from 50 tosses

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