252grass1-08(revised!!) 2/23/08
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. In diagrams of confidence intervals, shade
the interval. In diagrams of test ratios and critical values for a sample statistic, shade the ‘reject zone.
Problem 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)   3 , (ii)   3 , (iii)
  3 , (iv) x  3 , (v) p  0.3 , (vi) p  3 , (vii) s 2  3 , (viii)   3 , (ix)   3 (x)   3
Problem 2: A man walks into a bar. He drinks 10  a bottles of beer. These bottles are supposed to contain
12 ounces of beer with a population standard deviation of 0.4 ounces. On the basis of the man's condition
when he leaves the bar, we conclude that the total amount he drank was 115  13.5a ounces. Personalize the
data by replacing a by the second to last digit of your student number. If the second to last digit is zero,
a  10 . For example, Ima Badrisk has student number 012345, so a  4 and she claims that he drank 14
bottles of beer and a total of 115  13 .54  169 .0 . She then uses the total amount he drank and the total
number of bottles to compute a sample mean for the bottles.
Test the hypothesis that the population mean for these bottles was 12 ounces. 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. Hint: note that conclusions of b), c) and d) should be identical.
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 your test ratio and the Normal table. Use the p-value
to test the null hypothesis. Will you reject the null hypothesis with a confidence level of 10%? 5%?
1%? .002 (0.2%)? No answer will be accepted without a brief explanation.
Problem 3: Continue with your results from problem 2. We are still testing if the mean is 12.
a) Use the test ratio that you found on problem 2 to find an approximate p-value using the t-table
and assuming that 0.4 ounces was a sample standard deviation? Does this change any of your
results in 2e)?
b) Assume once again that 0.4 is a sample standard deviation. Test the hypothesis that the
population mean is 12 ounces. Show your ‘reject region on a diagram.   .05 .
c) i)Assume that 0.4 is a population standard deviation. Test the hypothesis that the population
mean is above 12 ounces using the test ratio that you found in 1d). State your null and alternative
hypotheses. Show your ‘reject region on a diagram.
ii) Perhaps this should have read ‘0.4 is a sample standard deviation.’ Lets try again.
d) Assume that 0.4 is a population standard deviation. Test the hypothesis that the population
mean is above 12 ounces using a critical value for the sample mean. State your null and alternative
hypotheses. Show your ‘reject region on a diagram.
e) Assume that 0.4 is a population standard deviation. Test the hypothesis that the population
mean is above 12 ounces using a one-sided confidence interval. Shade the confidence interval in
your diagram.
252grass1-08(revised!!) 2/23/08
Problem 4: (Steinberg) Supposedly at least 36% of college students change their major between freshman
year and graduation. You take a survey of 630 graduating seniors and find that 220  b changed their
majors, where b is the last digit of your student number. For example, Ima Badrisk has student number
12345, so b  5 and she claims that 220  b  220  5  225 changed their majors. Test the hypothesis.
a) State your null and alternative hypotheses.
b) Find a test ratio for a test of the proportion.
c) Make a diagram showing the rejection region for the test ratio if you use a 99% confidence
level.
d) Find a p-value for this ratio and use it to test the hypothesis at a 1% significance level
Extra Credit Problem 5:
a) Assume that the sample size is 20. 2 changed majors and you are testing the statement that at
least 40% changed majors. Do the test at the 90% confidence level without using the Normal
distribution.
The following data can be used in b) and c).
Make sure that your student number is easily readable. Choose one of the columns below using the second
to last digit of your Student Number. Example: Ima Badrisk has student number 123456; so she picks
column x5. Forget about the rest of the columns!
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
x0
2.3
7.9
11.5
2.1
9.1
5.8
2.7
12.0
0.6
-8.7
4.1
-0.6
-0.4
x1
8.8
2.9
2.5
6.5
3.4
-3.6
3.4
-1.5
11.5
16.1
4.6
1.4
4.4
x2
12.1
3.6
1.8
9.9
9.8
6.8
3.9
9.9
8.2
14.1
6.8
13.9
6.7
x3
5.7
5.7
2.8
2.9
1.2
6.8
0.3
9.6
3.8
0.7
9.3
9.4
6.1
x4
16.0
3.5
-1.7
6.8
8.9
4.1
-2.9
15.5
1.9
-0.9
3.0
2.8
4.1
x5
11.4
-4.6
4.7
-2.7
-3.6
-0.5
-1.2
-2.6
13.4
0.5
3.2
9.1
0.8
x6
3.3
3.5
12.2
-1.6
7.1
4.1
0.1
7.1
-1.5
1.0
6.2
1.7
-2.3
x7
-2.5
1.6
2.7
-0.8
-0.3
3.0
0.3
10.6
4.9
3.3
14.8
17.4
9.5
x8
6.7
1.7
2.0
10.5
4.6
11.3
6.7
4.1
5.2
3.7
9.9
4.9
9.7
x9
3.0
5.3
1.1
6.0
8.9
7.4
1.2
0.6
4.2
7.1
5.0
-2.5
8.8
b) Compute a sample standard deviation for your column and test the hypothesis   4
c) Using the same data, test the hypothesis that the median is below 4.
e) 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 630 220+b;
(Replace 220+b with the number you used.)
Test 0.36;
Conf 99;
(Sets a 99% confidence level)
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 for ‘number of trials’ and 220+b for ‘number of
events.’ Check ‘perform hypothesis test.’ Set ‘hypothesized proportion’ as 0.36. Press Options. Set
‘confidence level’ as 99, alternative hypothesis as ‘less than’ and check ‘Normal distribution.’ Go.
Third: Use the pull-down menu again. But before you start put 220+b yeses and 410+b noes in
column 1. (You should have 630 rows of data. You can do this entry very rapidly if you use
only y or 1 for yes and n or 0 for no. Just enter y 220+b times and then n until you get to row
630. Even better, put a zero in the first row and use the fill handle on the bottom right of the cell to
enter 1 an appropriate number of times then put a zero in the rest of the column the same way.)
Uncheck ‘summarized data’ and let Minitab know that the data are in column 1 (C1). Other
options are unchanged.
(Fourth: repeat your third try, but uncheck ‘Normal distribution.’)