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22 introduction to hypothesis testing 3 how

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Unformatted text preview: rnative hypotheses that we found in the previous lesson. Ho: Ha: 2 Suppose we randomly sampled 200 students at our college and found that 110 planned to vote. Thus 55% of the students in the sample planned to vote. Does this mean that more than half of all students at the college plan to vote? In order to determine the answer to this question we need to ask: “How unlikely would it be to find a random sample of size 200 in which 55% or more plan to vote, assuming the true population proportion is 50%?” The answer to this question is the P ­value. It turns out that the P ­value in this case is approximately 0.08. Interpret this P ­value. Look at the last paragraph under “Assess the Evidence” above for an example. © 2011 THE CARNEGIE FOUNDATION FOR THE ADVANCEMENT OF TEACHING A PATHWAY THROUGH STATISTICS, VERSION 1.6, STATWAY™  ­ STUDENT HANDOUT STATWAY STUDENT HANDOUT | 4 Lesson 8.2.2 Introduction to Hypothesis Testing 3 How does the P ­value compare to the level of significance, α = 0.05? Should we reject the null hypothesis? 4 What can we conclude about the claim? NEXT STEPS Errors in Hypothesis Tests It is possible that more than half of students at our college plan to vote, even though our hypothesis test did not support this claim. If it is the case that more than half of students plan to vote, but the evidence isn’t strong enough to support that conclusion, then the result of the hypothesis test is an error. In general, anytime we use sample evidence to make a decision about a hypothesis, there is a chance we will make the wrong decision. There are actually two types of errors that we can make. When we reject a null hyp...
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