Assignment No.4 (Course STA301)

Spring 2011 (Total Marks 30)

Deadline

Your Assignment must be uploaded/ submitted before or on

30^th June, 2011

STUDENTS ARE STRICTLY DIRECTED TO SUBMIT THEIR ASSIGNMENT BEFORE OR BY DUE DATE. NO ASSIGNMNENT AFTER DUE DATE WILL BE ACCEPTED VIA E.MAIL).

Rules for Marking

It should be clear that your Assignment will not get any credit IF:

The Assignment submitted, via email, after due date.
The submitted Assignment is not found as MS Word document file.
There will be unnecessary, extra or irrelevant material.
The Statistical notations/symbols are not well-written i.e., without using MathType software.
The Assignment will be copied from handouts, internet or from any other student’s file. Copied material (from handouts, any book or by any website) will be awarded ZERO MARKS. It is PLAGIARISM and an Academic Crime.
The medium of the course is English. Assignment in Urdu or Roman languages will not be accepted.
Assignment means Comprehensive yet precise accurate details about the given topic quoting different sources (books/articles/websites etc.). Do not rely only on handouts. You can take data/information from different authentic sources (like books, magazines, website etc) BUT express/organize all the collected material in YOUR OWN WORDS. Only then you will get good marks.

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)

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