252grass1-071 2/19/07
ECO 252 Second Graded Assignment
R. E. Bove
Name:
Class days and time:
Student Number:
Please include class and student number on what you hand in! Papers should be stapled. Your
writeup should state clearly what you did and concluded.
Problem 1: Which of the following could be a null hypothesis? Which could be an alternative hypothesis?
Which could be neither? Why?
(i) p  3 , (ii) p  .3 , (iii) p  .3 , (iv)   3 , (v)   3 , (vi)   3 , (vii) s  3 , (viii)  3 , (ix)   5 ,
(x) p  .3 , (xi)   3 , (xii)   0 ,(xiii) p  .5.
Problem 2: A rental firm believes that that the average time that a backhoe is rented is 4.2 days. In order to
verify this statement, a sample of rental records is taken, with the following results.
4, 2, 4, 3, 6, 2, 3, 2, 5, 3, 2, 4, 2, 2
You presumably know that n  14 , x  3.1429 , and  x  1 .1x . ( x is the last digit of your student
number.) Test the hypothesis that the mean is 4.2. Assume that the confidence level is 95%.
a) State your null and alternative hypotheses.
b) Find critical values for the sample mean and test the hypothesis. Show your reject region on a
diagram
c) Find a confidence interval for the sample mean and test the hypothesis. Show your results on a
diagram.
d) Use a test ratio for a test of the sample mean. Show your reject region on a diagram
e) Find a p-value for the null hypothesis using the Normal table and use the p-value to test the
hypothesis.
Problem 3: (Keller & Warrack) A random sample of 11 young adult men was asked how many minutes of
sports they watched daily. Results are below.
50
48
65
74
66
30
40
60
60
60
50
Personalize the data as follows: add the digits of your student number to the last six numbers. Example: Ima
Badrisk has the student number 123456; so the last six numbers become {31, 42, 63, 64, 65, 56}.
Compute the sample standard deviation using the computational formula (if you don’t know what
that means, find out!). (If you did this correctly on the last assignment, just copy your work.) Test the
hypothesis that average time watching sports is below 70 hours.
a) Test the validity of the hypothesis using a confidence level of 95% and a critical value for the
sample mean. (You cannot test the validity of a hypothesis that you haven’t stated!)
b) Find an approximate p-value for the statement.
c) Will we reject the hypothesis at a significance level of (i) .001? (ii) .01? (iii) .10? Using
the p-value explain why.
Note that none of the problems beyond this point involve sample means.
252grass1-071 2/19/07
Problem 4: (Ken Black) It is generally believed that 79% of US companies offer flexible scheduling . A
survey of 415 accounting firms finds that 300  x have flexible scheduling. ( x is the 2nd to last digit of your
student number.) Test the hypothesis that the proportion of accounting firms that offer flexible hours is
below that for other US firms.
a) State your null and alternative hypotheses.
b) Find a test ratio for a test of the proportion.
c) Find a p-value for this ratio and use it to test the hypothesis at a 5% significance level.
Extra Credit Problem 5:
a) Finish problem 4 by finding an appropriate confidence interval for the proportion and showing
whether it contradicts the null hypothesis.
b) Use the data in problem 3 to test the hypothesis   10 .
c) Use Minitab to check your answer to problem 4. Do this three ways
First: Enter Minitab. Use the Editor pull-down menu to enable commands. Then enter the
commands below.
Pone 415 300+ x ;
(Replace 300+x with the number you used.)
Test 0.79;
Alter -1;
(Makes H1 ‘less than.’)
useZ.
(Uses normal approx. to binomial)
Second: Use the Stat pull-down menu. Choose ‘Basic Stat’ and then ‘1 proportion.’
Check ‘summarized data’ and enter your n and 300+ x . Press Options. Set ‘test proportion’ as
0.79, alternative hypothesis as ‘less than’ and check ‘Normal distribution.’ Go.
Third: Use the pull-down menu again. But before you start put 10  x yesses and 50  x noes in
column 1. Uncheck ‘summarized data’ and let Minitab know that the data are in column 1 (C1).
Other options are unchanged.