Vuhelper
06-25-2011, 06:21 AM
Question 1: Marks:5+2+3=10
(a) Suppose we have two independent random variables X and Y. Let X follows Normal distribution with mean 0 and variance 4; Y also follows Normal distribution with mean 1and variance 9. A random sample of 10 observations is taken from each variable; then find .
(b) What will be the value of population standard deviation if the size of the simple random sample is 25 and standard error of the mean is 2?
(c) Why the Z test is usually inappropriate for small sample size? Give reasons in support of your answer.
Question 2: Marks:4+6=10
(a) When setting two sided ) %, confidence interval for , based on a random sample of size n from a normal population, how the following changes will effect the length of the confidence interval for (assuming all other quantities remain fixed)
• increasing
• increasing
• increasing
• decreasing n
(b) Suppose that the workers of factory B believe that the average income of the workers of factory A exceeds their average income. A random sample of workers is drawn from each of the two factories, and the two samples yield the following information:
Factory Sample Size Mean Variance
A 160 12.80 64
B 320 11.25 47
Test the above hypothesis? Also interpret your result.
Question 3: Marks:5+5=10
(a) In a random sample of 150 persons having their lunch at the University cafeteria on meatless day it was observed that 20 percent preferred vegetable dishes.
• Find 95% confidence interval for P (proportion of those who preferred vegetables)
• How large a sample is needed, if we want to be 98% confident that our estimate of P is within 0.01?
(b) Let denote a random sample from the Poisson distribution
Find the moment estimator of t.
(a) Suppose we have two independent random variables X and Y. Let X follows Normal distribution with mean 0 and variance 4; Y also follows Normal distribution with mean 1and variance 9. A random sample of 10 observations is taken from each variable; then find .
(b) What will be the value of population standard deviation if the size of the simple random sample is 25 and standard error of the mean is 2?
(c) Why the Z test is usually inappropriate for small sample size? Give reasons in support of your answer.
Question 2: Marks:4+6=10
(a) When setting two sided ) %, confidence interval for , based on a random sample of size n from a normal population, how the following changes will effect the length of the confidence interval for (assuming all other quantities remain fixed)
• increasing
• increasing
• increasing
• decreasing n
(b) Suppose that the workers of factory B believe that the average income of the workers of factory A exceeds their average income. A random sample of workers is drawn from each of the two factories, and the two samples yield the following information:
Factory Sample Size Mean Variance
A 160 12.80 64
B 320 11.25 47
Test the above hypothesis? Also interpret your result.
Question 3: Marks:5+5=10
(a) In a random sample of 150 persons having their lunch at the University cafeteria on meatless day it was observed that 20 percent preferred vegetable dishes.
• Find 95% confidence interval for P (proportion of those who preferred vegetables)
• How large a sample is needed, if we want to be 98% confident that our estimate of P is within 0.01?
(b) Let denote a random sample from the Poisson distribution
Find the moment estimator of t.