Question:
Let π1,π2,π5 be a random sample from a π΅ππ(1, π) distribution, where πβ(0,1) is an unknown parameter. For testing the null hypothesis π»0 βΆ πβ€ 0.5 against π»1 :π>0.5, consider the two tests π1 and π2 defined as:
π1: Reject π»0 if, and only if, \(β^5_{i=1}\) ππ=5.
π2: Reject π»0 if, and only if, \(β^5_{i=1}\) Xiβ₯3.
Let π½π be the probability of making Type-II error, at π=\(\frac{2}{3}\), when the test ππ , π=1,2 , is used. Then, the value of π½1+π½2 equals ________(round off to two decimal places)
Let π1,π2,π5 be a random sample from a π΅ππ(1, π) distribution, where πβ(0,1) is an unknown parameter. For testing the null hypothesis π»0 βΆ πβ€ 0.5 against π»1 :π>0.5, consider the two tests π1 and π2 defined as:
π1: Reject π»0 if, and only if, \(β^5_{i=1}\) ππ=5.
π2: Reject π»0 if, and only if, \(β^5_{i=1}\) Xiβ₯3.
Let π½π be the probability of making Type-II error, at π=\(\frac{2}{3}\), when the test ππ , π=1,2 , is used. Then, the value of π½1+π½2 equals ________(round off to two decimal places)
π1: Reject π»0 if, and only if, \(β^5_{i=1}\) ππ=5.
π2: Reject π»0 if, and only if, \(β^5_{i=1}\) Xiβ₯3.
Let π½π be the probability of making Type-II error, at π=\(\frac{2}{3}\), when the test ππ , π=1,2 , is used. Then, the value of π½1+π½2 equals ________(round off to two decimal places)
Updated On: Oct 1, 2024
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Correct Answer: 1.07
Solution and Explanation
The correct answer is: 1.07 to 1.09 (approx)
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