STA301 Assignment No. 4 solution
Thursday, June 30, 2011 Posted In STA Edit This Assignment No.4 (Course STA301)
Spring 2011 (Total Marks 30)
Deadline
Your Assignment must be uploaded/ submitted before or on
30th June, 2011
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Objective(s) of this Assignment:
The assignment is being uploaded to build up
- The concepts of students regarding the Application of sampling distributions in Estimation
- The students’ BASIC concept regarding the Estimation of parameters and Hypothesis testing
- To enable the students that how to check a of good point estimator for estimation purpose.
Assignment 4 (Lessons 31-38)
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)
) %, 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
denote a random sample from the Poisson distribution
Find the moment estimator of t.
SOLUTION:
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