For now suppose that in the random sample of 125

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Unformatted text preview: at least as extreme as the one found in our sample. This probability is a conditional probability (the condition is that the null hypothesis is true) and we call it a P ­value. We will see how to calculate P ­values for hypothesis tests for population means in Module 10. For now, suppose that in the random sample of 125 graduating students the sample standard deviation was 0.45. This would give a P ­value of about 0.002, or about 1 in 500. That is, there is roughly a 1 in 500 chance of getting a sample statistic like our, or more extreme, if the true mean GPA equals 2.50. In this case, the P ­value tells us that this sample mean is very unusual, assuming the null hypothesis is true. If the mean GPA for students graduating from our college is actually 2.50, a sample mean GPA of 2.62 or higher would occur in samples of size 125 only 0.2% of the time (or about 1 in 500 samples). State a Conclusion In order to reach a conclusion, we look at the strength of the evidence. The sample mean GPA of 2.62 would be an extremely unlikely sample result if the population mean GPA is actually 2.50. We can conclude that it is very unlikely that this sample came from a population with a mean GPA of 2.50. We can reject the null hypothesis and accept the alternative hypothesis in its place. We conclude a hypothesis test by stating a conclusion about the claim or research question being tested: The data provide strong evidence that the mean GPA for students graduating from our college is greater than 2.50 (P = 0.002). Notice that we included the P ­value in the conclusion. The P ­value gives the strength of the evidence against the null hypothesis. Including the P ­value allows the re...
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