Lesson_06_Notes

Lesson_06_Notes - Confidence Intervals

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Confidence Intervals Introduction Learning objectives for this lesson Upon completion of this lesson, you should be able to: Correctly interpret the meaning of confidence intervals Construct confidence intervals to estimate a population proportion Construct confidence intervals for estimate a population mean Calculate correct sample sizes for a study Recognize whether a given situation requires a proportion or means confidence interval Toward Statistical Inference Two designs for producing data are sampling and experimentation, both of which should employ randomization. As we have already learned, one important aspect of randomization is to control bias. Now we will see another positive. Because chance governs our selection (think of guessing whether a flip of a fair coin will produce a head or a tail) we can make use of probability laws – the scientific study of random behavior – to draw conclusions about an entire population from which the subjects originated. This is called statistical inference . We previously defined a population and a sample. Now we will consider what we use to describe their values. Parameter: a number that describes the population. It is fixed but we rarely know it. Examples include the true proportion of all American adults who support the president, or the true mean of weight of all residents of New York City. Statistic: a number that describes the sample. This value is known since it is produced by our sample data, but can vary from sample to sample. For example, if we calculated the mean heights of a random sample of 1000 residents of New York City this mean most likely would vary from the mean calculated from another random sample of 1000 residents of New York City. Examples 1. A survey is carried out at a university to estimate the proportion of undergraduate students who drive to campus to attend classes. One thousand students are randomly selected and asked whether they drive or not to campus to attend classes. The population is all of the undergraduates at that university campus. The sample is the group of 1000 undergraduate students surveyed. The parameter is the true proportion of all undergraduate students at that university campus who drive to campus to attend classes. The statistic is the proportion of the 1000 sampled undergraduates who drive to campus to attend classes. 2. A study is conducted to estimate the true mean yearly income of all adult residents of the state of California. The study randomly selects 2000 adult residents of California. The population consists of all adult residents of California. The sample is the group of 2000 California adult residents in the study. The parameter Confidence Intervals http://onlinecourses.science.psu.edu/stat200/book/export/html/46 1 of 8 9/27/2010 11:49 PM
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is the true mean yearly income of all adult residents of California. The statistic is the mean of the 2000 sampled adult California residents. Ultimately we will measure statistics and use them to draw conclusions about unknown parameters. This is statistical inference.
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This note was uploaded on 10/08/2010 for the course STAT 200 taught by Professor Barroso,joaor during the Fall '08 term at Penn State.

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Lesson_06_Notes - Confidence Intervals

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