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Q60Section C (Section C)60 of 60

Size plus power of a test on a Bernoulli sample

Let X1,X2,X3,X4X_1,X_2,X_3,X_4 be a random sample from a discrete distribution with the probability mass function P(X=0)=1−P(X=1)=1−pP(X=0)=1-P(X=1)=1-p, for 0<p<10<p<1. To test the hypothesis

H0:p=34againstH1:p=45,H_0:p=\frac34\quad\text{against}\quad H_1:p=\frac45,

consider the test: Reject H0H_0 if X1+X2+X3+X4>3X_1+X_2+X_3+X_4>3. Let the size and power of the test be denoted by α\alpha and γ\gamma, respectively. Then α+γ\alpha+\gamma (round off to 2 decimal places) equals __________

Numerical answer: type the number (no options).

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