# slide5 - a distribution for which the CLT applies. Find ,...

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1 Example: Propellant Burn Rate ± Aircrew escape systems are powered by a solid propellant. Specifications require that the mean burn rate must be 50 cm/s. ± H 0 : µ = 50 ± 10 samples are tested. 2 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

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3 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 4 Hypothesis Testing ± α = P(Type I error) = P(reject H 0 | H 0 is true) ± β = P(Type II error) = P(accept H 0 | H 0 is false) No error Type I error Reject H 0 Type II error No error Fail to reject H 0 H 0 is false H 0 is true Decision
5 Example Part (1) ± Suppose the acceptance region is 48.5 ≤≤ 51.5 ± Suppose that the burn rate has a standard deviation of 2.5 cm/s, and has

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Unformatted text preview: a distribution for which the CLT applies. Find , P(Type I error) What are some ways to reduce ? x 6 Example Part (2) Suppose it is important to reject the null hypothesis when >52 or <48. Let the alternate hypothesis, H 1 : = 52 Find , P(Type II error) What affects the size of ? 7 Interlude Type I error can be directly controlled: rejecting the null hypothesis is a strong conclusion . Type II error depends on sample size and the extent to which the null hypothesis is false: accepting the null hypothesis is a weak conclusion . The power of a test is the probability of rejecting the null hypothesis when the alternative hypothesis is true, i.e., 1 . The P-value is the smallest level of significance that would lead to rejection of the null hypothesis....
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## This note was uploaded on 05/05/2008 for the course IE 121 taught by Professor Perevalov during the Spring '08 term at Lehigh University .

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slide5 - a distribution for which the CLT applies. Find ,...

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