Robert_V._Hogg,_Joseph_W._McKean,_Allen_T._Craig
4.4. Order Statistics 265 4.4.19.LetXandYdenote independent random variables with respective proba- bility density functionsf(x) ...
266 Some Elementary Statistical Inferences (a)P(Y 1 <ξ 0. 5 <Y 5 ). (b)P(Y 1 <ξ 0. 25 <Y 3 ). (c)P(Y 4 <ξ 0. 80 & ...
4.5. Introduction to Hypothesis Testing 267 4.5 IntroductiontoHypothesisTesting................... Point estimation and confiden ...
268 Some Elementary Statistical Inferences Table 4.5.1: 2 ×2 Decision Table for a Hypothesis Test True State of Nature Decision ...
4.5. Introduction to Hypothesis Testing 269 Over all critical regions of sizeα, we want to consider critical regions that have l ...
270 Some Elementary Statistical Inferences power is higher to detect the alternativep=0.2thanp=0.6. In Section 8.2, we prove in ...
4.5. Introduction to Hypothesis Testing 271 cance levelof the test associated with that critical region. Moreover, sometimes αis ...
272 Some Elementary Statistical Inferences So if we have some reasonable idea of whatσequals, we can compute the approxi- mate p ...
4.5. Introduction to Hypothesis Testing 273 Table 4.5.2:Plant Growth Pot 12345678 Cross 23.500 12.000 21.000 22.000 19.125 21.50 ...
274 Some Elementary Statistical Inferences and define the critical region to beC={(x 1 ,x 2 ):^34 ≤x 1 x 2 }.Findthepower functi ...
4.6. Additional Comments About Statistical Tests 275 4.5.11.LetY 1 <Y 2 <Y 3 <Y 4 be the order statistics of a random s ...
276 Some Elementary Statistical Inferences Example 4.6.1(Large Sample Two-Sided Test for the Mean).In order to see how to constr ...
4.6. Additional Comments About Statistical Tests 277 Consider again the situation at the beginning of this section. Suppose we w ...
278 Some Elementary Statistical Inferences that is, we acceptH 0 at significance levelαif and only ifμ 0 is in the (1−α)100% con ...
4.6. Additional Comments About Statistical Tests 279 Example 4.6.4.LetX 1 ,X 2 ,...,X 10 be a random sample of sizen=10froma Poi ...
280 Some Elementary Statistical Inferences Consider, first, the one-sided hypothesesH 0 :μ=μ 0 versusH 1 :μ>μ 0 ,whereμ 0 is ...
4.6. Additional Comments About Statistical Tests 281 For thep-value, compute each of the one-sidedp-values, take the smallerp-va ...
282 Some Elementary Statistical Inferences 15.92 16.58 17.57 16.75 17.28 17.32 17.51 17.58 18.26 17.87 rival: 15.95 16.15 17.05 ...
4.7. Chi-Square Tests 283 4.6.8.Letpequal the proportion of drivers who use a seat belt in a country that does not have a mandat ...
284 Some Elementary Statistical Inferences which has, asn→∞, an approximateN(0,1) distribution (see Theorem 4.2.1). Furthermore, ...
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