Question: b) Let Y1, Y2, ..., Y20 be a random sample from a normal distribution with unknown mean u and known variance o = 7. We

b) Let Y1, Y2, ..., Y20 be a random sample from a normal distribution with unknown mean u and known variance o = 7. We wish to test Ho: u = 19 versus H1: u > 19. The rejection region is y > C(a). Find the most powerful test with significance level 5%. NB: No need not to derive the likelihood test for part b. (4 marks)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

a. Suppose YI,Y2,...,Y5 are independent normal random variables with mean, 6 and variance, :93 > 0 . Name the distribution and its parameters of: (2 marks) (2 marks) $qu _ 9) v02 iii. Determine the...

Refer to Exercises 8.88.10. Show that the rejection region for the likelihood ratio test is given by Z > z ,where P(Z > z ) = . Under the assumption that H O : = 0 is true, show that n (y) is a...

Refer to Exercise 8.8. Suppose we want to test H o : = 0 against the alternative H a : > 0. Since the estimator of is = y, the likelihood ratio test statistic is Show that Use the fact that n...

Refer to Exercise 8.8 and 8.9. Show that the rejection region is equivalent to the rejection region y y , where P( ) and P(y y ) = . Use the fact that e -a2 0 as |a| . Data from...

2.1 A cellular call is made to your cell phone at random within a ten-minute interval. You were busy on a call for 2 minutes into this ten-minute period. There is a probability that the call arrived...

Hi, it's me again Thanks for helping me with the answer last time d u 1. (a) Let Y1, Y2, ..., Yn be a random sample from a Bernoulli (p) distribution (i.e. Binomial(1, p)). Show ELI K is a minimal...

Solve the question below kindly How many chords can be drawn through 21 points on a circle? 4. How many triangles can be formed by joining the vertices of a hexagon? 5. Out of 7 consonants and 4...

Suppose that X1, . . . , X11 form a random sample from the normal distribution with unknown mean 1 and unknown variance 21 . Suppose also that Y1, . . . , Y21 form an independent random sample from...

Normal Distribution Consider a random sample of size T, {y1, y2, , yT }, of iid random variables from the normal distribution with unknown mean and known variance 2 0 = 1 f(y; ) = 1 2 exp (y ...

CO, elsewhere. b Find the MVUE of 0. 9.64 Let Y1, Y2, . .., Y, be a random sample from a normal distribution with mean / and variance 1. a Show that the MVUE of /? is /2 - Y" - 1. b Derive the...

A $9,500 bond that carries a 3.00% coupon rate payable semi-annually is purchased 5 years before maturity when the yield rate was 4.50% compounded semi-annually. a. Calculate the purchase price of...

Refer to Data Set 12 in Appendix B, and use the heights of U.S. Presidents and the heights of their main opponents in the election campaign. Does there appear to be a correlation? Construct a scatter...

Derrick purchased a fee simple interest in the interior of a cottage on the lake with an interest in the parking area, recreation center, laundry room, and docks. What kind of ownership interest did...

Tommy offered to sell his baseball card collection to Frank for $ 1 0 , 0 0 0 , a fair value. While Frank was considering the offer, Tommy's house floods and the baseball cards are damaged by the...

Revenue recognition. JCPenney uses the accrual basis of accounting and recognizes revenue at the time it sells goods. Indicate the amount of revenue the firm recognizes during the month of May in...

Revenue recognition. Assume that a firm uses the accrual basis of accounting and recognizes revenue at the time it sells goods or renders services. Indicate the amount of revenue the firm recognizes...

Expense recognition. Indicate the effect on assets and the amount of expense recognized (if any) by Computervision from each of the following related events, assuming that the firm uses the accrual...