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# notes 32 - Hypothesis Testing for a Proportion Submitted by...

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Hypothesis Testing for a Proportion Submitted by gfj100 on Wed, 11/11/2009 - 13:15 Ultimately we will measure statistics (e.g. sample proportions and sample means) and use them to draw conclusions about unknown parameters (e.g. population proportion and population mean). This process, using statistics to make judgments or decisions regarding population parameters is called statistical inference. Example 2 above produced a sample proportion of 47% heads and is written: [read p-hat] = 47/100 = 0.47 P-hat is called the sample proportion and remember it is a statistic (soon we will look at sample means, .) But how can p-hat be an accurate measure of p, the population parameter, when another sample of 100 coin flips could produce 53 heads? And for that matter we only did 100 coin flips out of an uncountable possible total! The fact that these samples will vary in repeated random sampling taken at the same time is referred to as sampling variability. The reason sampling variability is acceptable is that if we took many samples of 100 coin flips an calculated the proportion of heads in each sample then constructed a histogram or boxplot of the sample proportions, the resulting shape would look normal (i.e. bell-shaped) with a mean of 50%. [The reason we selected a simple coin flip as an example is that the concepts just discussed can be difficult to grasp, especially since earlier we mentioned that rarely is the population parameter value known. But most people accept that a coin will produce an equal number of heads as tails when flipped many times.] A statistical hypothesis test is a procedure for deciding between two possible statements about a population. The phrase significance test means the same thing as the phrase "hypothesis test." The two competing statements about a population are called the null hypothesis and the alternative hypothesis. A typical null hypothesis is a statement that two variables are not related. Other examples are statements that there is no difference between two groups (or treatments) or that there is no difference from an existing standard value. An alternative hypothesis is a statement that there is a relationship between two variables or there is a difference between two groups or there is a difference from a previous or existing standard. NOTATION

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notes 32 - Hypothesis Testing for a Proportion Submitted by...

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