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Hypothesis testing, types of hypotheses, errors in hypothesis

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STAT 301
Brett Hunter

30 September Hypothesis Testing Hypothesis testing is a method for using sample data to decide between two competing claims (hypotheses) about a population characteristic. A hypothesis is a statement about the value of a population parameter developed for the purpose of testing. e.g. The mean salary for ALL graduates of four-year business schools is $2,200 per month. The mean monthly income for ALL systems analysts is at least $3,625. Less than twenty percent of ALL juvenile offenders are caught and sentence to prison. Types of hypotheses Null hypothesis – A claim about a population characteristic that is initially assumed to be true. Denoted H . 0 Alternative hypothesis – The competing claim. Denoted H or H . A 1 In carrying out a test of H 0ersus H , tAe hypothesis H will 0e rejected in favor of H only ifA sample evidence strongly suggests that H is fal0e. Two possible conclusions Reject H a0d claim H is tAue Fail to reject H 0 Note: Failing to reject H 0s not the same as saying H is tr0e. We just do not have enough evidence to claim that it is false. Hypothesis for tests comparing a parameter to a value The alternative hypothesis has the following forms HA: population characteristic < hypothesized value HA: “ > “ H A “ ≠ “ The null corresponding to above is H 0 population characteristic ≥ hypothesized value H 0 “ ≤ “ H : “ = “
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