Question: Suppose that X1, . . . , Xn form a random sample from the normal distribution with known mean 0 and unknown variance 2, and

Suppose that X1, . . . , Xn form a random sample from the normal with known mean 0 and unknown variance σ2, and suppose that it is desired to test the following hypotheses:
H0: σ2 ≤ 2,
H1: σ2 > 2.
Show that there exists a UMP test of these hypotheses at every level of significance α0 (0 < α0 < 1).

Step by Step Solution

★★★★★

3.35 Rating (173 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

We know from Exercise 2 that the joint pdf of X 1 X n has a monotone likelihood ratio in ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

602-M-S-H-T (3846).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Personal Relationship O Criminal Intent Q.13. What type of Workplace Violence does this scenario match? Scenario: An Emergency Department patient kicks the attending doctor in the chest...

A function y = f(x) is defined as follows: y = f(x) 1.0 1.025 1.049 1.072 Compute the values of dyldx and vidr at x =1.05. X 1.0 1.05 1.10 1.15 X 1.20 1.25 1.30 y = f(x) 1.095 1.118 1.140

Suppose that X1,..., Xn is a random sample from a n(, 2) population. a. If 2 is known, find a minimum value for n to guarantee that a .95 confidence interval for n will have length no more than /4....

Suppose that X1 and X2 form a random sample of two observed values from the exponential distribution with parameter . Show that X1/(X1 + X2) has the uniform distribution on the interval [0, 1].

Suppose that X1, . . . , Xn form a random sample from the normal distribution with mean and variance 2, and let denote the sample variance. Determine the smallest values of n for which the following...

Suppose that X1, . . . , Xn form a random sample from the normal distribution with mean and variance 2, and Y is an independent random variable having the normal distribution with mean 0 and...

Suppose that X1, . . . , Xn form a random sample from the normal distribution with mean 0 and unknown standard deviation > 0. Find the lower bound specified by the information inequality for the...

Suppose that X1, . . . , Xn form a random sample from the normal distribution with mean and variance 2, where both and 2 are unknown. A confidence interval for is to be constructed with confidence...

Suppose that X1, . . . , Xn form a random sample from the normal distribution with mean and variance 2. Find the distribution of n(Xn )2/2.

Assume that X1, . . . , Xn form a random sample from the normal distribution with mean and variance 2. Show that has the gamma distribution with parameters (n 1)/2 and n/(22).

Suppose that X1, . . . , Xn form a random sample from the normal distribution with unknown mean and known variance 2. Suppose also that the prior distribution of is normal with mean and variance...

Discuss the social determinants of health and how the affect older adults

In a random sample of 220 potential voters registered in the state of Maryland, 86 indicated that they planned to vote in the next general election. In an independently chosen, random sample of 287...

E9.27 A unity feedback system has a loop transfer function G M . . = 8 dB. (b) Determine the value of gain K and cross over frequency for marginal stability. K L(s) =G(s)G(s) = s(s+3) (a) Determine...

A shot putter releases the shot some distance above the level ground with a velocity of 12.0 m/s, 51.00 above the horizontal. The shot hits the ground 2.08 s later. You can ignore air resistance. (a)...

An airplane is flying with a velocity of 90.0 m/s at an angle of 23.0o above the horizontal. When the plane is 114 m directly above a dog that is standing on level ground, a suitcase drops out of the...

A pistol that fires a signal flare gives it an initial velocity (muzzle velocity) of 125 m/s at an angle of 55.0 above the horizontal. You can ignore air resistance. Find the flare's maximum height...

A particularly long traffic light on your morning commute is green 20% of the time that you approach it. Assume that each morning represents an independent trial. (a) Over five mornings, what is the...

A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof 1.00 s later. You may ignore air resistance. (a) If the height of the building is 20.0 m,...

Establishing price for an outsourcing decision Lunn Company makes and sells lawn mowers for which it currently makes the engines. It has an opportunity to purchase the engines from a reliable...

Let $X_{1}, X_{2}$, and $X_{3}$ be independent normal variables with \[\begin{array}{lll}E\left(X_{1} ight)=-4 & \text { and } & \sigma_{1}^{2}=1 \\E\left(X_{2} ight)=0 & \text { and } &...

Refer to Exercise 6.36. (a) Show that $2 X_{1}-X_{2}-4 X_{3}-12$ has a normal distribution. (b) Find the mean and variance of the random variable in part (a). Data From Exercise 6.36 6.36 Let X1,...

Let $X_{1}, X_{2}$, and $X_{3}$ be independent normal variables with \[\begin{array}{lll}E\left(X_{1} ight)=5 & \text { and } & \sigma_{1}^{2}=9 \\E\left(X_{2} ight)=-2 & \text { and } &...

Dividends paid by a corporation to its stockholders are tax deductible by the corporation, but interest paid on bonds is not tax deductible. True or False True False

[The following information applies to the questions displayed below.) Each of the following situations is independent d Special-Order Pricing Barry's Bar-B-Que is a popular lunch-time spot. Barry is...

Humble Management Services opened for business and completed these transactions in September. Sep. 1 Henry Humble, the owner, invested $38,000 cash along with office equipment valued at PROBLEM SET B...