Question

Suppose we have a random sample of size 50 from a N(μ,σ2) PDF. We wish to...

Suppose we have a random sample of size 50 from a N(μ,σ2) PDF. We wish to test H0: μ=10 versus H1: μ=10. The sample moments are x ̄ = 13.4508 and s2 = 65.8016. (a) Test the null hypothesis that σ2 = 64 versus a two-sided alternative. First, find the critical region and then give your decision. (b) (5 points) Find a 95% confidence interval for σ2? (c) (5 points) If you are worried about performing 2 statistical tests on the same data and that the overall type I error might not be 5%, how might you modify your approach?

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
Suppose we have a random sample of size 50 from a N(μ,σ2) PDF. We wish to...
Suppose we have a random sample of size 50 from a N(μ,σ2) PDF. We wish to test H0: μ=10 versus H1: μ=10. The sample moments are x ̄ = 13.4508 and s2 = 65.8016. (a) Find the critical region C and test the null hypothesis at the 5% level. What is your decision? (b) What is the p-value for your decision? (c) What is a 95% confidence interval for μ?
Let X1,.....,Xn be a random sample from N(μ,σ2), and both μ and σ2 are unknown, with...
Let X1,.....,Xn be a random sample from N(μ,σ2), and both μ and σ2 are unknown, with -∞<μ<∞ and σ2 > 0. a. Develop a likelihood ratio test for H0: μ <= μ0 vs. H1: μ > μ0 b. Develop a likelihood ratio test for H0: μ >= μ0 vs. H1: μ < μ0
A random sample is obtained from a population with a variance of σ2=200, and the sample...
A random sample is obtained from a population with a variance of σ2=200, and the sample mean is computed to be x̅c=60. Test if the mean value is μ=40. Test the claim at the 10% significance (α=.10). Consider the null hypothesis H0: μ=40 versus the alternative hypothesis H1:μ≠40 The distribution of the mean is normal N = 100.
Suppose we take a random sample X1,…,X6 from a normal population with an unknown variance σ2...
Suppose we take a random sample X1,…,X6 from a normal population with an unknown variance σ2 and unknown mean μ. Construct a two-sided 99% confidence interval for μ if the observations are given by 2.59,0.89,2.69,0.04,−0.26,1.31
1. For a particular scenario, we wish to test the hypothesis H0 : μ = 14.9....
1. For a particular scenario, we wish to test the hypothesis H0 : μ = 14.9. For a sample of size 35, the sample mean X̄ is 12.7. The population standard deviation σ is known to be 8. Compute the value of the test statistic zobs. (Express your answer as a decimal rounded to two decimal places.) 2. For a test of H0 : μ = μ0 vs. H1 : μ ≠ μ0, assume that the test statistic follows a...
A random sample of size n=16 is take from a normal population with μ=40 and σ2=32....
A random sample of size n=16 is take from a normal population with μ=40 and σ2=32. Find the probability that the sample mean is greater than or equal to 38.
To test H0​: μ=50 versus H1​: μ<50​, a simple random sample of size n=26 is obtained...
To test H0​: μ=50 versus H1​: μ<50​, a simple random sample of size n=26 is obtained from a population that is known to be normally distributed. Answer parts​ (a)-(c). ​(a) If x overbar =47.3 and s=13.1​, compute the test statistic. t= _________ ​(Round to two decimal places as​ needed.) (b) Draw a​ t-distribution with the area that represents the​ P-value shaded. Determine whether to use a​ two-tailed, a​ left-tailed, or a​ right-tailed test. c) Approximate the​ P-value.
Using a random sample of size 77 from a normal population with variance of 1 but...
Using a random sample of size 77 from a normal population with variance of 1 but unknown mean, we wish to test the null hypothesis that H0: μ ≥ 1 against the alternative that Ha: μ <1. Choose a test statistic. Identify a non-crappy rejection region such that size of the test (α) is 5%. If π(-1,000) ≈ 0, then the rejection region is crappy. Find π(0).
suppose that we are testing H0:μ=μ0 versus H1:μμ0 with a sample size of n=10. calculate bounds...
suppose that we are testing H0:μ=μ0 versus H1:μμ0 with a sample size of n=10. calculate bounds on the P-value for the following observed values of the test statistic: a)t0 =2.48 b)t0=-3.95 c)t0=2.69 d)t0=1.88 e) t0=-1.25 Please show how the values were found Engineering statistics 5th edition question 4-48
A sample of size 10 is taken from the first population: Sample mean of 101.2 and...
A sample of size 10 is taken from the first population: Sample mean of 101.2 and sample variance of 18.1 A sample of size 14 is taken from the second population: Sample mean of 98.7 and sample variance of 9.7 a)In order to decide whether pooling is appropriate or not, performing a test at α = 0.2 level of significance : Find the rejection region. b)In order to decide whether pooling is appropriate or not, performing a test at α...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT