What is the Type I error probability of this test?

MATLAB: An Introduction with Applications
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What is the Type I error probability of this test?
Transcribed Image Text:What is the Type I error probability of this test?
Suppose that we have an independent and identically distributed sample from some distribution
family G defined by an unknown parameter value 1. We are testing the hypotheses
H,:A = 1 versus Ha:A = 2.
Our test statistic is T, and let T have an Expo(1) distribution. The Expo(1) probability density
function (pdf) and cumulative distribution function (cdf), respectively, are
fr(t) = le-a for t >0
Fr(t) = 1- e-dt for t > 0
The rejection region for this hypothesis test is {T < 0.5}.
Transcribed Image Text:Suppose that we have an independent and identically distributed sample from some distribution family G defined by an unknown parameter value 1. We are testing the hypotheses H,:A = 1 versus Ha:A = 2. Our test statistic is T, and let T have an Expo(1) distribution. The Expo(1) probability density function (pdf) and cumulative distribution function (cdf), respectively, are fr(t) = le-a for t >0 Fr(t) = 1- e-dt for t > 0 The rejection region for this hypothesis test is {T < 0.5}.
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