252grass2-072 9/19/07
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.
1. Which of the following could be null hypotheses? Which could be an alternate hypothesis? Which could
be neither? Why? If some of these are valid null hypotheses, state the alternate. If some of these are valid
alternative hypotheses, state the null. Label H 0 and H 1 clearly. (i) p  1.2, (ii) p  .3
(iii)   0.35, (iv)   3 (v) x  1.22 , (vi)   3 (vii)   0.45, (viii) s  0.45, (ix)   25 , (x)
  1005 .37 .
Problem 2: A Federal agency is checking weights of an ‘8 ounce’ container of a product. A random sample
of 13 bottles is taken. Results are below.
7.81
7.92
7.94
8.00
7.95
7.91
7.98
8.05
8.17
7.80
7.80
7.80
7.90
Personalize the data as follows: change the last digit of the weights of the last three bottles to the
last three digits of your student number. Example: Ima Badrisk has the student number 123456; so the last
three numbers become {7.84, 7.85, 7.96}.
Compute the sample standard deviation using the computational formula. (Even better copy it from
Grass 1!). Test the hypothesis that the mean is below 8 ounces. Assume that the confidence level is
90%.
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 one-sided 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: Continue with your results from Problem 2.
a) Will we reject the null hypothesis in problem 2 at a significance level of (i) .001? (ii) .01? (iii)
.10? Using the p-value explain why..
b) Use the mean that you found in Problem 2, a known population standard deviation of 0.20 and
test the hypothesis that the mean is 8 using a 95% confidence level and a critical value or values
for the sample mean. (You cannot test the validity of a hypothesis that you haven’t stated!)
c) Find an approximate p-value for the statement.
d) Will we reject the hypothesis in 3b 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.
Problem 4: (Kazmier) A university placement director assers that at least 50% of seniors had found jobs
by April 1. A random sample of 50 seniors is polled and 15  a  of these students indicate that they have
jobs. Personalize the sample results by using the last digit of your student number as a . Test the truth of
directors claim using a 90% confidence level.
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 1% significance level.
252grass2-072 9/19/07
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. Use a 90% confidence level.
b) Assume that the sample size is 10 and 2 have jobs. Repeat the test at the 90% confidence level
without using the Normal distribution.
c) Use the data in problem 1 to test the hypothesis   0.20.
d) Using your data in Problem 1, test the hypothesis that the median is below 7.95 ounces.
e) Use Minitab to check your answer to problem 4. Do this three ways. (I’ll explain this later.)