Question

A sample from a Normal distribution with an unknown mean µ and known variance σ =...

A sample from a Normal distribution with an unknown mean µ and known variance
σ = 45 was taken with n = 9 samples giving sample mean of ¯ y = 3.6.


(a) Construct a Hypothesis test with significance level α = 0.05 to test whether the
mean is equal to 0 or it is greater than 0. What can you conclude based on the
outcome of the sample?
(b) Calculate the power of this test if the true value of the mean is µ = 3.
(c) Construct the Most Powerful Hypothesis test with significance level α = 0.05 for
testing H 0 : µ = 0 vs H a : µ = 3.
(d) Is this test also Uniformly Most Powerful Hypothesis test for testing H 0 : µ = 0
vs H a : µ > 0? Justify.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A sample data is drawn from a normal population with unknown mean µ and known standard...
A sample data is drawn from a normal population with unknown mean µ and known standard deviation σ = 5. We run the test µ = 125 vs µ < 125 on a sample of size n = 100 with x = 120. Will you be able to reject H0 at the significance level of 5%? A. Yes B. No C. Undecidable, not enough information D. None of the above
Suppose X1, · · · , Xn from a normal distribution N(µ, σ2 ) where µ...
Suppose X1, · · · , Xn from a normal distribution N(µ, σ2 ) where µ is unknown but σ is known. Consider the following hypothesis testing problem: H0 : µ = µ0 vs. Ha : µ > µ0 Prove that the decision rule is that we reject H0 if X¯ − µ0 σ/√ n > Z(1 − α), where α is the significant level, and show that this is equivalent to rejecting H0 if µ0 is less than the...
Problem 1. A random sample was taken from a normal population with unknown mean µ and...
Problem 1. A random sample was taken from a normal population with unknown mean µ and unknown variance σ2 resulting in the following data. 10.66619, 10.71417, 12.12580, 12.09377, 12.04136, 12.17344, 11.89565, 12.82213, 10.13071, 12.35741, 12.48499, 11.79630, 11.32066, 13.53277, 11.20579, 11.39291, 12.39843 Perform a test of H0 : µ = 10 versus H1 : µ ≠10 at the .05 level. Do the data support the null hypothesis?
Let X1, X2, . . . , Xn be a random sample from the normal distribution...
Let X1, X2, . . . , Xn be a random sample from the normal distribution N(µ, 36). (a) Show that a uniformly most powerful critical region for testing H0 : µ = 50 against H1 : µ < 50 is given by C2 = {x : x ≤ c}. Find the values of c for α = 0.10.
Suppose we observe Y1,...Yn from a normal distribution with unknown parameters such that ¯ Y =...
Suppose we observe Y1,...Yn from a normal distribution with unknown parameters such that ¯ Y = 24, s2 = 36, and n = 15. (a) Find the rejection region of a level α = 0.05 test of H0 : µ = 20 vs. H1 : µ 6= 20. Would this test reject with the given data? (b) Find the rejection region of a level α = 0.05 test of H0 : µ ≤ 20 vs. H1 : µ > 20....
To test H0: µ = 42.0 vs. HA: µ ≠ 42.0, a sample of n =...
To test H0: µ = 42.0 vs. HA: µ ≠ 42.0, a sample of n = 40 will be taken from a large population with σ= 9.90. H0 will be rejected if the sample mean is less than 40.3 or greater than 43.7. Find and state the level of significance, α, to three (3) places of decimal.
A random sample is selected from a normal population with a mean of μ=50 and a...
A random sample is selected from a normal population with a mean of μ=50 and a standard deviation of σ=12. After a treatment is administered to the individuals in the sample, the sample mean is found to be M=55. a. If the sample consists of n=16 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α =0.05. b. If the sample consists of n=36 scores, is the sample mean...
Use µ = 2.5 and σ = 1 to generate many independent sets of ten random...
Use µ = 2.5 and σ = 1 to generate many independent sets of ten random numbers, each. If I were to repeatedly carry out the one-sample t-test and significance level α = 0.05 to test the hypothesis that the mean µ used to generate those random numbers was µ = 2.5 for each new vector of ten numbers, how often, on average, would you expect to reject the null hypothesis? Explain how you come to your conclusion.
A random sample is selected from a normal population with a mean of µ = 30...
A random sample is selected from a normal population with a mean of µ = 30 and a standard deviation of σ= 8. After a treatment is administered to the individuals in the sample, the sample mean is found to be x̅ =33. Furthermore, if the sample consists of n = 64 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05. 4a. Which of the following...
A sample of size 20 is drawn from a normal distribution with unknown variance and unknown...
A sample of size 20 is drawn from a normal distribution with unknown variance and unknown mean µ. The sample mean is ¯ x = 1.25 and the sample standard deviation is s = 0.25. The 99% lower confidence bound on µ is A. 1.108 ≤ µ B. 1.120 ≤ µ C. µ ≤ 1.392 D. µ ≤ 1.380
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT