A single observation is to be used to test the nullhypothesis that the mean waiting time between tremors recorded at a seismological station (the mean of an expo-nential population) is θ = 10 hours against the alternative that θ Z 10 hours. If the null hypothesis is to be rejected ifand only if the observed value is less than 8 or greaterthan 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.

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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 expo-
nential population) is θ = 10 hours against the alternative

that θ Z 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.

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