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Midterm

Steps of hypothesis testing, p-values

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Department
Statistics
Course
STAT 301
Professor
Brett Hunter
Semester
Fall

Description
3 October α = P(Type I Error) (level of significance) β = P(Type II Error) After assessing the consequences of Type I and Type II errors, we identify the largest α that is tolerable for the problem. We then employ a test procedure that uses α as the maximum acceptable Type I error rate. Comments Generally, with everything else held constant, decreasing one type of error increases the other. The only way to decrease both types of errors is to increase the sample size. No matter what decision is reached through a hypothesis test, there is always the risk of one of these errors. Definitions Test statistic – a numeric function of sample data on which a conclusion to reject or fail to reject H0is based P-value – the probability of obtaining a test statistic as extreme or more extreme than the one calculated, assuming H is t0ue A decision to reject H 0s found by comparing the p-value to α. If p-value ≤ α, H 0s rejected If p-value > α, H is not rejected 0 Steps of Hypothesis Testing (7-step procedure) State the set of hypotheses that correspond to the research question of interest in terms of the population parameter(s). H /H 0 A Select the significance level α. This is the cut-off point for deciding if the probability is small enough (i.e., is p-value small enough?
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