Let X1, , Xn be a random sample from an N (, 2) Assume that 2 is unknown We wish to test, at level a, H0 0 versus Ha 0 Find an appropriate LRT

Question: Let X1, . . ., Xn be a random sample from an N (, 2). Assume that 2 is unknown. We wish to test, at

Let X1, . . ., Xn be a random sample from an N (μ, σ2). Assume that σ2 is unknown. We wish to test, at level a, H0: μ = μ0 versus Ha: μ < μ0. Find an appropriate LRT.

Step by Step Solution

★★★★★

3.32 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Here and Hence Similarly for the alt... 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)

610-M-S-H-T (3395).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let X1, X2,..., Xn be a random sample from an exponential distribution with parameter . Then it can be shown that 2Xi has a chi-squared distribution with v = 2n (by first showing that 2Xi has a...

Let X1,..., Xn be a random sample from a n(Î¼, Ï2) population, where both Î¼ and Ï2 are unknown. Each of the following methods of finding confidence intervals for...

Let X1,.., Xn be a random sample from a population with mean Î¼ and variance Ï2. (a) Show that the estimator is an unbiased estimator of Î¼ if (b) Among all unbiased...

Let X1,..., Xn be a random sample from a n(, 2) population. (a) If is unknown and 2 is known, show that Z = n( - 0)/ is a score statistic for testing H0: = 0. (b) If 2 is unknown and is known,...

Let X1,..., Xn be a random sample from a n(, 2) population. (a) If is unknown and 2 is known, show that Z = n( - 0)/ is a Wald statistic for testing H0: = 0. (b) If 2 is unknown and is known, find...

Let X1,..., Xn be a random sample from a n(, 2) population. Consider testing H0: 0 versus H1 : > 0. Let m denote the sample mean of the first m observations, X1,... ,Xm, for m = l,...,n. If 0 +...

4. Let X1, ..., Xn be a random sample from an N(u, 2). Assume that o is known. At level a, we test Ho : M = Mo, VS. Ha : u > Mo. The likelihood ratio test (LRT) is defined as: 1 = maxuEe. L(0; X1,...

Let X1,..., Xn be a random sample from a n((, 2) population. Compare expected lengths of 1 - confidence intervals for that are computed assuming 2 is known. 2 is unknown.

This exercise will prove the assertions in Example 7.2.16, and more. Let X1,..., Xn be a random sample from a n(, 2) population, and suppose that the prior distribution on is n(, 2). Here we assume...

4 Mathematics 341/686 December 8, 2015 1. Let X1 , X2 , . . . , Xn be a random sample from N (1 , 2 ) and let Y1 , Y2 , . . . , Yn be a random sample from N (2 , 2 ) and 2 is known. (a) Find the...

What are the variables of a regression analysis, and how do they affect the results of the analysis? What challenge does this pose to getting reliable results?

Which of the following options is one of the roots of the latitude? 4 = 3 denkleminin kklerinden biri aadaki klarn hangisinde verilmitir? O ei cos( z) + i sin( 67 O cos cos() () + i sin 4 4 O -1

APPLE T Use an applet for the tornado damage data. The One-Variable Statistical Calculator applet on the text CD and Web site will make stemplots and histograms. It is intended mainly as a learning...

Discuss the switching costs that Southwest Airlines would incur if it began to phase out its fleet of Boeing airliners with replacements from Airbus. What steps could Airbus take to reduce these...

(from Hamming26) A game is played as follows: A random number X is chosen uniformly from [0, 1]. Then a sequence Y1, Y2, . . . of random numbers is chosen independently and uniformly from [0, 1]. The...

In a certain manufacturing process, the (Fahrenheit) temperature never varies by more than 2o from 62o. The temperature is, in fact, a random variable F with distribution (a) Find E (F) and V (F)....

A number is chosen at random from the integers 1, 2, 3, . . . , n. Let X be the number chosen. Show that E(X) = (n+1)/2 and V (X) = (n−1)(n+1)/12. Hint: The following identity may be useful:...

Discussion Question: Review of key economic models contributing to global public health Which models are most appropriate for tracking health care trends in low income countries

Period obs1 obs2 obs3 obs4 Sample Mean Sample Range 1 0.48 0.49 0.51 0.5 0.495 0.03 2 0.46 0.45 0.45 0.49 0.4625 0.04 3 0.51 0.53 0.45 0.51 0.5 0.08 4 0.48 0.46 0.55 0.49 0.495 0.09 5 0.48 0.5 0.52...

Data were collected from a sample of 220 patients concerning whether or not they had a certain condition and results from a blood test for the condition. Rows: Health status Columns: Blood test...