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# notes 33 - Hypothesis Testing for a Mean Submitted by...

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Hypothesis Testing for a Mean Submitted by gfj100 on Wed, 11/11/2009 - 13:16 Quantitative Response Variables and Means We usually summarize a quantitative variable by examining the mean value. We summarize categorical variables by considering the proportion (or percent) in each category. Thus we use the methods described in this handout when the response variable is quantitative. Again, examples of quantitative variables are height, weight, blood pressure, pulse rate, and so on. Null and Alternative Hypotheses for a Mean For one population mean, a typical null hypothesis is H 0 : population mean μ = a specified value. We'll actual give a number where it says "a specified value," and for paired data the null hypothesis would be H 0 : u d = a specified value. Typically when considering differences this specified value is zero The alternative hypothesis might either be one-sided ( a specific direction of inequality is given) or two-sided ( a not equal statement). Test Statistics The test statistic for examining hypotheses about one population mean : where the observed sample mean, μ 0 = value specified in null hypothesis, s = standard deviation of the sample measurements and n = the number of differences. Notice that the top part of the statistic is the difference between the sample mean and the null hypothesis. The bottom part of the calculation is the standard error of the mean. It is a convention that a test using a t-statistic is called a t-test. That is, hypothesis tests using the above would be referred to as "1-sample t test". Finding the p-value Recall that a p -value is the probability that the test statistic would "lean" as much (or more) toward the alternative hypothesis as it does if the real truth is the null hypothesis. When testing hypotheses about a mean or mean difference, a

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