14.2.10. Suppose that a random sample of size 36, Y, Y2, ..., Y36, is drawn from...

Question

Question

Answer 1

Answer #1

14.2.10.

Let &1/4 be true 25th percentile then Null hypothesis, Ho: €1/4 = 6 vs. Alternative hypothesis, Hq : 61/4 + 1/4 Let S = no. o

When &1/4 = 7 then s 4 N (36 * (3/14) = 7.7143, (36 * (3/14) * (11/14) = 2.4620). P(Type II error($1/4 = 7) = P(3.9078 < s <

Answer 2

Similar Homework Help Questions

Suppose that a random sample of size 36, Y1,Y2,...,Y36, is drawn from a uniform pdf de...

Suppose that a random sample of size 36, Y1,Y2,...,Y36, is drawn from a uniform pdf de ned over the interval (0, θ), where θ is unknown. Set up a large- sample sign test for deciding whether or not the 25th per- centile of the Y -distribution is equal to 6. Let α = 0.05. With what probability will your procedure commit a Type II error if 7 is the true 25th percentile?
QUESTION 3 Let Y1, Y2, ..., Yn denote a random sample of size n from a...

QUESTION 3 Let Y1, Y2, ..., Yn denote a random sample of size n from a population whose density is given by (Parcto distribution). Consider the estimator β-Yu)-min(n, Y, where β is unknown (a) Derive the bias of the estimator β. (b) Derive the mean square error of B. , Yn).
2. [x] Suppose that Y1, Y2, Y3 denote a random sample from an exponential distribution whose...

2. [x] Suppose that Y1, Y2, Y3 denote a random sample from an exponential distribution whose pdf and cdf are given by f(y) = (1/0)e¬y/® and F(y) =1 – e-y/0, 0 > 0. It is also known that E[Y;] = 0. ', y > 0, respectively, with some unknown (a) Let X = min{Y1,Y2, Y3}. Show that X has pdf given by f(æ) = (3/0)e-3y/º. Start by thinking about 1- F(x) = Pr(min{Y1,Y2, Y3} > x) = Pr(Y1 > x,...

Problem 2: Let Y, Y2,. Y2o form a random sample of size n Determine the joint...

Problem 2: Let Y, Y2,. Y2o form a random sample of size n Determine the joint pdf of (Y, Y2, 20 from Exp(B) population. Ya).
FR2 (4+4+4 12 points) (a) Let XI, X2, X10 be a randoin sample from N(μι,σ?) and Yi, Y2, 10 , Y 15 be a random sample from N (μ2, σ2), where all parameters are unknown. Sup- pose Σ 1 (Xi X 2 0 321 (Y-...

FR2 (4+4+4 12 points) (a) Let XI, X2, X10 be a randoin sample from N(μι,σ?) and Yi, Y2, 10 , Y 15 be a random sample from N (μ2, σ2), where all parameters are unknown. Sup- pose Σ 1 (Xi X 2 0 321 (Y-Y )2-100. obtain a 99% confidence interval for σ of having the form b, 0o) for some number b (No derivation needed). (b) 60 random points are selected from the unit interval (r:0 . We want...
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS θ for the purpose of testing Ho : θ-2 against H, : θ < 2 at α : 0.10 level of significance. Suppose the decision rule is to be...

A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS θ for the purpose of testing Ho : θ-2 against H, : θ < 2 at α : 0.10 level of significance. Suppose the decision rule is to be based on Xmax, the largest order statistic. What would be the probability of committing a Type II error when θ 1.7. A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS...

54.2. Suppose X is a random sample of size n = 1 from a uniform distribution...

54.2. Suppose X is a random sample of size n = 1 from a uniform distribution defined on the interval (0, e). Construct a 98% confidence interval for θ and
7. (1 point) Let X be the mean of a random sample of size 36 from...

7. (1 point) Let X be the mean of a random sample of size 36 from the uniform distribution U(7,15) Find P(11.3 <X < 11.5)
5. Let Yi,Y2, , Yn be a random sample of size n from the pdf (a)...

5. Let Yi,Y2, , Yn be a random sample of size n from the pdf (a) Show that θ = y is an unbiased estimator for θ (b) Show that θ = 1Y is a minimum-variance estimator for θ.

A simple random sample of size n is drawn. The sample mean, x, is found to...

A simple random sample of size n is drawn. The sample mean, x, is found to be 19.4, and the sample standard deviation, s, is found to be 4.9. Click the icon to view the table of areas under the t-distribution. (a) Construct a 95% confidence interval about if the sample size, n, is 35. Lower bound: :Upper bound: (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about if the sample size,...