252x0312 2/12/03
ECO252 QBA2
FIRST HOUR EXAM
February 20, 21 2003
Show your work! Make Diagrams!
I. (8 points) Do all the following.
x ~ N 11,3
x  16
1. P
2.
P11  x  16
3. F
4.
10
x.125
(The cumulative probability up to 10)
Name ___________________
Hour of class registered _____
Class attended if different ____
252x0312 2/12/03
II. (5 points-2 point penalty for not trying part a.)
A random sample is taken of the endowments of private colleges in the US. The following data is
found.
College
1
2
3
4
Endowment
($Millions)
60
47
235
3909
a. Compute the sample standard deviation, s , of the endowments. Show your work! (3)
b. Compute a 99% confidence interval for the mean endowment,  .(3)
2
252x0312 2/12/03
III. Do all of the following Problems (17 points) Show your work except in multiple choice questions.
1. Which of the following would be an appropriate null hypothesis (1)?
a) The population proportion is less than 0.65.
b) The sample proportion is less than 0.65.
c) The population proportion is no less than 0.65.
d) The sample proportion is no less than 0.65.
TABLE 9-1
Microsoft Excel was used on a set of data involving the number of parasites
found on 46 Monarch butterflies captured in Pismo Beach State Park. A
biologist wants to know if the mean number of parasites per butterfly is
over 21. She will make her decision using a test with a level of 0.10. The
following information was extracted from the Microsoft Excel output for the
sample of 46 Monarch butterflies:
n = 46; Arithmetic Mean = 29.00; Standard Deviation = 25.92; Standard
Error = 3.82;
Null Hypothesis: H 0 :   21.000 ;  = 0.10; df = 45; T Test Statistic
= 2.09;
One-Tailed Test Upper Critical Value = 1.301; p-value = 0.021; Decision
= Reject.
2.
3.
4.
Referring to Table 9-1, the parameter the biologist is interested in is (1):
a) the mean number of butterflies in Pismo Beach State Park.
b) the mean number of parasites on these 46 butterflies.
c) the mean number of parasites on Monarch butterflies in Pismo Beach State Park.
d) the proportion of butterflies with parasites.
Referring to Table 9-1, Mark the following true or false (3):
a) The null hypothesis would be rejected if a 5% probability of committing a Type I error is
allowed.
b) The null hypothesis would be rejected if a 2% probability of committing a Type I error is
allowed.
c) The null hypothesis would be rejected if a 1% probability of committing a Type I error is
allowed.
Referring to Table 9-1, state the alternate hypothesis for this study (1).
3
252x0312 2/12/03
5. The marketing manager for an automobile manufacturer is interested
in determining the proportion of new compact-car owners who would
have purchased a passenger-side inflatable air bag if it had been
available for an additional cost of $290. The manager believes from
previous information that the proportion is 0.30. Suppose that a
survey of 200 new compact-car owners is selected and 76 indicate that
they would have purchased the inflatable air bags. If you were to conduct a
test to determine whether there is evidence that the proportion is different from 0.30, which test would
you use? (1)
2
a)  -test of population variance.
b) z-test of a population mean
c) z-test of a population proportion
d) t-test of population mean
6. In problem 5, using a 5% significance level when appropriate:
a) State the null and alternative hypotheses (2)
b) Do the problem using a test ratio (3)
c) Find a p-value for the test ratio (1)
d) Do the problem using a confidence interval (2)
e) Do the problem using a critical value for a proportion (2)
f) (Extra credit) Remember what you did on page 1 and do e) again using a 25%
significance level (2)
7. We believe that the standard deviation for household income per year in Hooverville is $2900. We
take a sample of n  150 households and find a sample standard deviation of $2600.
a) Test the hypothesis that the population standard deviation is $2900 assuming that the
underlying distribution is Normal. (2)
b) (Extra credit) Do a confidence interval for the population standard deviation.(2)
c) (Extra credit) Test the hypothesis that the population standard deviation is less than
$2900. (2)
4
252x0312 2/12/03
ECO252 QBA12
FIRST EXAM
February 20, 21 2003
TAKE HOME SECTION
Name: _________________________
Social Security Number: _________________________
IV. Do the first two problems (at least 10 each) (or do sections adding to at least 20 points - Anything extra
you do helps, and grades wrap around) . Show your work! State H 0 and H 1 where appropriate. You
have not done a hypothesis test unless you have stated your hypotheses, run the numbers and stated
your conclusion. Use a 95% confidence level unless another level is specified.
1. (Kazmier) You want to be sure that the set-up time for new equipment is not more than 9 minutes for
each hour of operation. From a random sample of 40 hours selected from the records of another company
that has already bought the equipment, we find a sample mean of 10.09 minutes. Assume a population
standard deviation of 3.00 minutes. Use a 99% confidence level.
a) State your null and alternative hypotheses. (1)
b) Find a critical value for the sample mean and specify where your ‘reject’ region is (a diagram
is suggested) (1)
c) Do you reject the null hypothesis? Show why. (1)
d) Create a power curve for this test. (6)
e) Do a 2-sided confidence for the mean (1)
f) (Extra credit) It is possible to determine the required sample size in a one-sided test for the
mean given certain levels of the probability of a type I and a type II error. If  0 is the
population mean from the null hypothesis and we want to be able to keep the probability of a
type II error to  when the mean is actually 1 , use the following sample size:
n
z
 z   2
2

1   0 2
. Assume that
  .01 ,   .05
and that
1  9.1. Show that we
will need a much larger sample size than was proposed. (3)
2. (Kazmier) A company takes a random sample of 100 men in a large community and finds that 42% prefer
its blades.
a) Create a 95% confidence interval for the proportion that favor the blade. (2)
b) How large a sample would we need if the proportion must be known within  .05 ? (3)
c) Assume that the company is testing the hypothesis that the proportion is greater than or equal
to 45%, find a critical value for the sample proportion and use it to test the hypothesis using the
data at the beginning of this problem. (2)
d) What would the p-value be in for your hypothesis in c) if (i) the sample proportion was .44 and
(ii) the sample proportion was .46? (3)
e) (Extra credit) Assume that the actual proportion is 43%, what is the power of the test in c)? (3)
3. A new product assembly system is introduced and we are trying to find out if the median number of units
assembled per workshift is larger than the 80 units per workshift we got under the old system. The following
data is assembled on the number of units assembled in a workshift.
75, 85, 92, 80, 94, 90, 91, 76, 88, 82, 96, 83
a) Test the hypothesis that the median is above 80 at the 5% level. (4)
b) (Extra credit) Use the second highest number and the second lowest number to create a twosided confidence interval and find its significance level. (3)
c) Lets say that you had a sample of 150 numbers and that 100 were above 80. Repeat a). (2)
d) If you have 150 numbers and took two numbers at an equal distance (in Order) from the
highest and lowest to create an approximately 95% confidence interval for the median, what
would they be?
5