It is known that the random variable 𝑌 has a probability density function 𝑓(𝑦; 𝜃) = {
Posted: Fri Nov 26, 2021 8:29 am
It is known that the random variable 𝑌 has a probability density function
𝑓(𝑦; 𝜃) = {
𝜃𝑦
𝜃−1
, 0 < 𝑦 < 1
0, 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒
It is desired to test the null hypothesis 𝐻0: 𝜃 = 2 against the alternative 𝐻1: 𝜃 = 1.
A random sample 𝑌1 of size 𝑛 = 1 is to be used.
i) Calculate the level of significance or type I error which rejects 𝐻0 if 𝑌1 ≤
1
2
. (4)
𝑓(𝑦; 𝜃) = {
𝜃𝑦
𝜃−1
, 0 < 𝑦 < 1
0, 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒
It is desired to test the null hypothesis 𝐻0: 𝜃 = 2 against the alternative 𝐻1: 𝜃 = 1.
A random sample 𝑌1 of size 𝑛 = 1 is to be used.
i) Calculate the level of significance or type I error which rejects 𝐻0 if 𝑌1 ≤
1
2
. (4)