=========================preview======================
(MATH144)[2004](f)midterm~4660^_93574.pdf
Back to MATH144 Login to download
======================================================

MATH 244 Applied Statistics


Mid-Term Test II I November 30, 2004




Please read the following instructions carefully before you begin the exam.


1. Do not begin until you are told to do so.

2. Please place your student identity card on your desk for verification purposes.

3. There are 4 questions in this test. You have to answer all questions. Please write down all your answers in your answer book. Show all your works.



4. You will have 1 hour and 30 minutes to complete the exam.

5. No books, notes or other reading materials are permitted. Some formulae and statistics tables that you may need are provided.

6. If you feel you need to think a lot for a question, skip it and return to it later. Some of the easiest question for you might be at the very end. So, choose your own order of answering the questions.

7. Anyone who is caught cheating, helping someone cheat, or who is suspected of cheating, will receive zero mark on this exam. There will be no exception.

8. Do your best, and good luck!!!




















































1. (32 marks) To determine the effectiveness of a feed supplement for cattle, High-Grade Feeds conducts a pilot study. Twenty steers are randomly divided into a group of 10 steers to be fed the supplement, and another group of 10 steers to be fed exactly the same diet except for the supplement. The weight gains (lbs) over a period of 6 months were measured and summarized below.

Group
Mean
Standard Deviation

Supplement
359
66.32

Control
293
35.24



Suppose steers wholesale $7 per pound and the supplement costs $900 per steer for the whole 6-month period.

(a)
Are the variations of weight gains significantly different in the supplement group and control group? Test with 10% significant level.
(6 marks)




(b)
If you believe that the supplement is effective in increasing the weight gains of cattle, what hypotheses should you test, in terms of
(average weight gains by diets with supplement) and
(average bacteria by diets without supplement)?
(4 marks)




(c)
Test your hypothesis in (b) with 5% significant level. What can be concluded?
(6 marks)




(d)
State the assumption(s) you had made in the tests in part (a) and part (c).
(4 marks)




(e)
Construct a 95% confidence interval for
. Is it profitable to use the supplement? Explain briefly.
(6 marks)




(f)
How many steers should be used in the experiment if we want the confidence interval in part (e) to have length no longer than 80 lbs?
(6 marks)






P. T. O.
2. (20 marks) Explain the following terms.
(a)
Confidence level
(5 marks)




(b)
Significance probability
(5 marks)




(c)
Statistical mo