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Unformatted text preview: 1 Tests of Hypotheses about the mean  continued 2 Reminder Two types of hypotheses : H the null hypothesis (e.g. =24) H 1 the alternative hypothesis (e.g. &gt;24) Test statistic: Pvalue: probability of obtaining values as extreme as or more extreme than the test statistic e.g., P(Z2)=0.0228 Decision at the significance level: Reject H if pvalue&lt; n X Z  = 2 100 3 24 4 . 23 : e.g. = = Z 3 Testing hypotheses using a confidence interval: Example: A certain maintenance medication is supposed to contain a mean of 245 ppm of a particular chemical. If the concentration is too low, the medication may not be effective; if it is too high, there may be serious side effects. The manufacturer takes a random sample of 25 portions and finds the mean to be 247 ppm. Assume concentrations to be normal with a standard deviation of 5 ppm. Is there evidence that concentrations differ significantly (=5%) from the target level of 245 ppm? Hypotheses: H : =245 H 1 : 245 4 First, lets examine the Z test statistic: Test statistic: Pvalue: 2P(Z&gt;2)=2(0.0228)=0.0456 Decision at 5% significance level : Pvalue&gt; reject H0 The concentration differs from 245 = = n X Z 2 25 5 245 247 = 5 Now, examine the hypotheses using a confidence interval =0.05 confidence level is 1 = 95% 95% CI: [245.04 , 248.96] We are 95% certain that the mean concentration is between 245.04 and concentration is between 245....
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This note was uploaded on 11/03/2009 for the course IST IST taught by Professor N/a during the Spring '09 term at Anadolu University.
 Spring '09
 N/A

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