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A single observation is to be used to test the null hypothesis that the mean waiting time between tremors recorded at a seismological station (the mean of an exponential population) is θ = 10 hours against the alternative that θ 10 hours. If the null hypothesis is to be rejected if and only if the observed value is less than 8 or greater than 12, find
(a) the probability of a type I error;
(b) the probabilities of type II errors when θ = 2, 4, 6, 8, 12, 16, and 20.
Also plot the power function of this test criterion.
The same students increased their scores on a retest to: 85,79,75,95, and 84. At the 0.05 significance level, is the intervention plan helpful in increasing grades?
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For some of the attributes in your computer decision, you face uncertainty. The additive utility function assessed in Problem 15.17 essentially assumes that additive independence among attributes is reasonable.
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