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Solution) Let X_1,X_2,...,{{X}_{10}} be a random sample from an exponential random variable with density f(x)=

Question: Let \({{X}_{1}},{{X}_{2}},...,{{X}_{10}}\) be a random sample from an exponential random variable with density \(f\left( x \right)=\lambda {{e}^{-\lambda x}}\) on x > 0. How would you test \({{H}_{0}}:\lambda =0.20\) versus \({{H}_{a}}:\lambda =0.25\) at the level of significance \(\alpha =0.05\) ?

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