7. You have one observation Y , which has one of the discrete pdf’s
y f0(y) f1(y) 0 0.1 0.3 1 0.1 0.1 2 0.1 0.1 3 0.1 0.2 4 0.2 0.1 5
0.1 0.1 6 0.3 0.1 You want to test H0 : f0 is true Ha : f1 is true
(a) Here is a test: reject H0 if Y = 0, 1, 2, 3, or 5. What are the
probabilities of the two types of error for this test? What is the
power of the test at the alternative? (b) What is the most powerful
test for H0 against Ha of level α = 0.1? What is the most powerful
test of level α = 0.2?
Here we have given a observation which has discrete pdfs.
Find the attached images for detailed solutions of the questions.
Thank You!!
7. You have one observation Y , which has one of the discrete pdf’s y f0(y)...
1. Consider two probability density functions on [0,1]: f0(x) = 3x2 and f1(x) = 4x3. a.) Construct the most powerful test for H0 : X ~ f0 against HA : X ~ f1 with the significance level alpha = 0.1 b.) Find its power.
Please show work. Thanks in advance.
Question 5 (20 pts) You must decide which of two discrete distri- butions a random variable X has. We will call the distributions po and p. Here are the probabilities they assign to the values r of X. 2 Po P 0 1 2 0.1 0.1 0.2 0.1 0.3 0.2 3 4 5 0.3 0.1 0.1 0.1 0.1 0.1 6 0.1 0.1 You have a single observation on X and wish to test Ho:...
You have observed one observation X from a distribution with probability density function fx (x) and support X = {x : 0 〈 x 〈 1} (a) Derive the most powerful α 0.05 test for testing Ho : fx(x) = 2x 1 (0 < x < 1) versus H1 : fx (x) = 5c4 1 (0 〈 x 〈 1). Be sure to give the rejection region explicitly. (b) Compute the power of the test
You have observed one observation...
There are 5 black, 3 white, and 4 yellow balls in a box (see picture below). Four balls are randomly selected with replacement. Let M be the number of black balls selected. Find P[M =2]. A) Less than 10% B) Between 10% and 30% C) Between 30% and 43% D) Between 43% and 60% E) Bigger than 60%. Use the following information to answer Q19 and Q20: You must decide which of two discrete distributions a random variable X has....
5. Suppose Y represents a single observation from the probability density function given by: Soyo-1, 0, 0<y<1 elsewhere Find the most powerful test with significance level a=0.05 to test: HO: 0=1 vs. Ha: 0=2.
Let X have one of the following distributions: X H0 HA x1 .2 .1 x2 .3 .4 x3 .3 .1 x4 .2 .4 a. Compare the likelihood ratio, , for each possible value X and order the xi according to . b. What is the likelihood ratio test of H0 versus HA at level α = .2? What is the test at level α = .5? c. If the prior probabilities are P(H0) = P(HA), which outcomes favor H0? d....
You read that a statistical test at the α=0.01 level has probability 0.14 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative? Suppose we tested the null hypothesis that the weight of a McDonald's quarter pounder is 0.25 pounds (H0 : µ = 0.25) against the alternative that the weight is below 0.25 pounds (Ha : µ < 0.25). After collecting a sample our observed z statistic...
You read that a statistical test at the α=0.01 level has probability 0.14 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative? Suppose we tested the null hypothesis that the weight of a McDonald's quarter pounder is 0.25 pounds (H0 : µ = 0.25) against the alternative that the weight is below 0.25 pounds (Ha : µ < 0.25). After collecting a sample our observed z statistic...
1. You are told that .coin has probability of a Head either p 1/3 or p = 2/3. You must a test Ho p= Ha p You toss the coin 3 times and get Y Heads. You decide to reject Ho in favor of Ha if Y = 2 or Y 3. (Note that the count of Heads Y is the CSS for p.) What are the two error probabilities a and B for this test? What is the power...
6. (4 points) Suppose n = 82. How much is σˆ 2 , the estimated
variance of the error term ui?
A. 0.00625
B. 0.0125
C. 0.025
D. 0.05
7. (4 points) Suppose βˆ 1 = 0.75, SE(βˆ 1) = 0.01 and n = 52.
Then the 90% confidence interval for βˆ 1 would be
A. [0.4224, 1.1994]
B. [0.6112, 0.9112]
C. [0.7336, 0.7664]
D. [0.7229, 0.7661]
8. (4 points) Suppose one tested and rejected the null
hypothesis H0 :...