Question

Let 𝑋1,𝑋2,𝑋5 be a random sample from a 𝐵𝑖𝑛(1, 𝜃) distribution, where 𝜃∈(0,1) is an unknown parameter. For testing the null hypothesis 𝐻0 ∶ 𝜃≤ 0.5 against 𝐻1 :𝜃>0.5, consider the two tests 𝑇1 and 𝑇2 defined as:
𝑇1: Reject 𝐻0 if, and only if, $∑^5_{i=1}$ 𝑋𝑖=5.
𝑇2: Reject 𝐻0 if, and only if, $∑^5_{i=1}$ Xi≥3.
Let 𝛽𝑖 be the probability of making Type-II error, at 𝜃=$\frac{2}{3}$, when the test 𝑇𝑖 , 𝑖=1,2 , is used. Then, the value of 𝛽1+𝛽2 equals ________(round off to two decimal places)

Answer 1

The correct answer is: 1.07 to 1.09 (approx)