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Unformatted text preview: 1 Hypothesis testing: example An automotive company claims that its new motorcycle produces 145 hp at the rear wheel. It is known that the standard deviation for the whole population is equal to 3 hp. Let’s take several size 10 samples and try to find out whether the statement can be trusted. Given a value of the sample mean suggest a criterion according to which the claim (hypothesis) can be rejected. How easy is it to reject a true claim? 2 Hypothesis testing If the true average horsepower is equal to 144, how easy is it to fail to reject the false claim? What happens with the error probabilities if we vary the rejection criteria? In practice, it is convenient to start from a given probability of the error of the first type, and set the critical values accordingly. It is also handy to standardize the sample mean and compare directly with z. 3 Definitions Critical region : range of values for which the null hypothesis is rejected Acceptance region : range of values for which the null hypothesis is not rejected Critical values : boundaries between the critical and acceptance regions 4 More Definitions Type I error : rejecting the null hypothesis when it is true Type II error : failing to reject the null hypothesis when it is false Significance level : probability of type I error 5 Hypothesis Testing α = P(Type I error) = P(reject H  H is true) β = P(Type II error) = P(accept H  H is false) Decision H is true H is false Fail to reject H No error Type II error Reject H Type I error No error 6 Hypothesis Tests on the Mean H : μ = μ H 1 : μ ≠ μ n X Z σ μ = 2 / 2 / 2 / 2 / z Z z if H reject to Fail z Z or z Z if H Reject α α α α ≤ ≤ < 7...
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This note was uploaded on 03/17/2008 for the course IE 121 taught by Professor Perevalov during the Spring '08 term at Lehigh University .
 Spring '08
 Perevalov

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