252x0411 2/25/04
ECO252 QBA2
Name ___________________
FIRST HOUR EXAM Hour of class registered _____
February 25 2004
Class attended if different ____
Show your work! Make Diagrams! Exam is normed on 50 points. Answers without reasons are not
usually acceptable.
I. (8 points) Do all the following.
x ~ N 1,7 
1. P1  x  25 .5
2. P0  x  16 
3. F 25 .5 (The cumulative probability up to 25.5)
4.
x.015
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II. (5 points-2 point penalty for not trying part a.)
A random sample is taken of the time spent waiting in line at a bank. The following data is found.
(Recomputing what I’ve done for you is a great way to waste time.)
x
x2
1
2
3
4
5
6
7
8
9
10
11
Sum
5
3
6
2
7
1
3
4
2
10
2
45
25
9
36
4
49
1
9
16
4
100
4
257
a. Compute the sample standard deviation, s , of the waiting times. Show your work! (2)
b. Compute a 90% confidence interval for the mean,  .(3)
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III. Do all of the following Problems (17+ points) Show your work except in multiple choice questions.
Questions are 2 points each unless otherwise noted.
1.
(Lee) We want to test whether the weight of an average bag of cat food is above 50 pounds at a 5%
significance level. What are our null and alternative hypotheses?
a) H 0 :   50 and H 1 :   50
b) H 0 :   50 and H 1 :   50
H 0 :   50 and H 1 :   50
d) * H 0 :   50 and H 1 :   50
e) H 0 :   50 and H 1 :   50
f) H 0 :   50 and H 1 :   50
c)
2.
(Lee) We want to test whether the weight of an average bag of cat food is above 50 pounds at a 5%
significance level. We take a sample of 144 and find a sample mean of 49 and a sample standard
deviation of 5. What is the value of our t or z test ratio?
a) -2.0
b) -2.5
c) -2.4
d) -2.8
e) -3.0
3.
(Lee)A company wishes to test the volume of fuel in a 50 gallon drum. Since the company assumes
that it is being cheated it uses H 0 :   50 . Assume   .01 and that from a sample of 31 it gets a
sample mean and a sample standard deviation of 1.1 gallons. From the results of the sample it
x  50
computes the ratio
. It should do the following:
 1.1 




 31 
a) Reject H 0 if the ratio is below -2.576.
b) Reject H 0 if the ratio is below -2.327.
c)
Reject H 0 if the ratio is below -2.750.
d) Reject H 0 if the ratio is below -2.457.
e)
Reject H 0 if the ratio is below -2.576 or above 2.576.
f) Reject H 0 if the ratio is above one of the numbers in a-d.
g) None of the above – supply correct value or values.
4.
(Lee)The price paid by students at an WCU for a new textbook is believed to be Normally
distributed with a population standard deviation of $15.75. A random sample of 50 students has a
sample mean of $47.80. A 90% confidence interval for the population mean is:
a) $44.14 to $51.46
b) $43.04 to $52.56
c) $46.34 to $53.66
d) $44.10 to $51.50
e) $45.06 to $50.54
5.
In problem 4, is the price paid by students in the sample significantly different from $44.12? (1)
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6.
The head of an accounting department wants to test to see if the proportion of bad invoices is
below 0.1%. She examines 10000 invoices (, finds 4 bad ones) and tries to test the null hypothesis
with a confidence interval. The appropriate confidence interval is.:
.001 .999 
a) p  .0004  1.960 
10000
b)
p  .0004  1.960 
c)
p  .0004  1.645 
d)
p  .0004  1.645 
e)
.0004 .9996 
10000
.0004 .9996 
10000
.0004 .9996 
10000
None of the above – write in correct interval.
7.
We wish to test that the median is above 39. If p is the proportion above 35, the correct null
hypothesis is
a) p  .5
b) p  .5
c) p  .5
d) None of the above.
8.
(Lee) A reporter wants to poll people about an upcoming election. From previous polls, the
proportion of people favoring the incumbent president is about .6. The reporter will be satisfied if
the error of estimation is less than .04 with a confidence level of 90%. How many people should be
polled?
a) 167
b) 372
c) 260
d) 347
e) 406
8a. (Extra Credit) In section 8.7 of the text, the authors present sample size determination using the
n0 N
finite population correction factor. Equation (8.14) says that n 
. Assume that your
n0  N  1
answer to Problem 8 is correct and use this to adjust your answer to problem 8 when the country has
only 1000 voters.
9.
(Lee) A sample of size 30 is taken from a Normally distributed population. The sample standard
deviation is 4 and we use the 5% significance level. Which of the following (Circle one or more!)
are (is) true? (3)
a) If the null hypothesis is H 0 :   5 , it will be rejected.
b) If the null hypothesis is H 0 :   5 , it will not be rejected.
c)
If the null hypothesis is H 0 :   5 , it will be rejected.
d) If the null hypothesis is H 0 :   5 , it will not be rejected.
e)
If the null hypothesis is H 0 :   5 , it will be rejected.
f)
If the null hypothesis is H 0 :   5 , it will not be rejected.
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ECO252 QBA12
4
FIRST EXAM
February 25 2004
TAKE HOME SECTION
Name: _________________________
Student Number and class: _________________________
IV. Do at least 3 problems (at least 7 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. You are an investment advisor and wants to determine the suitability of the residents of a retirement
community as a clientele. You take a random sample of 10 incomes from the community and get the
following data (in thousands of dollars): 606 498 529 547 500 475 487 497 628 561.
Before you go any further, make your own unique data set by replacing the last digit of each of the first six
numbers with the digits of your Student number. For example, Seymour Butz’s student number is 976500,
so he will change the data to 609 497 526 545 500 470 487 497 628 561.
You want to check whether the mean income is above $500 thousand. Work in thousands. Use a
95% confidence level.
a. Find the sample mean and sample standard deviation of the incomes in your data, showing
your work. (1)
b. State your null and alternative hypotheses (1)
c. Test the hypothesis using a test ratio (1)
d. Test the hypothesis using a critical value for a sample mean. (1)
e. Test the hypothesis using a confidence interval (1)
f. Find an approximate p-value for the null hypothesis. (1)
g. On the basis of your tests, should you decide to sell advising in this community? (1)
h. (Extra credit) Actually the data I used came from a skewed distribution. So assume that you
expand your random sample to 12 by adding the following data points: 501 619. (Seymour’s
data would now read 609 497 526 545 500 470 487 497 628 561 501 619.) and test
that the median is above 500. (3)
2. Continue with the hypotheses of Problem 1. Instead of the sample standard deviation you found in
Problem 1 assume that the population standard deviation is 50. Use the sample mean that you found in
question 1.
a. Find a p-value for the null hypothesis. (1)
b. Create a power curve for the test. (95% confidence level) (6)
3.
a. Using the sample standard deviation that you found in question 1, test the hypothesis that the
standard deviation is above 48.(1)
b. Test that the standard deviation equals 48. (1)
c. Do a 2-sided confidence interval for the standard deviation (1)
d. (Extra Credit) Test the hypothesis that the standard deviation is above 48 using a confidence
interval. (2)
e. Create a two sided confidence interval for the mean using a the sample mean you found, a
population standard deviation of 50 and a confidence level of 97%. (2)
f. Assume that you wanted to create a 99% confidence interval for the mean income with an error
of 2 (thousand) , how large a sample would you need? Assume that the population standard
deviation is 50. (1)
g. With some illustrative calculations show the effect on the size of the sample you need in f) of
(i) a higher confidence level and (ii) a larger population variance. (2)
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4.
a. Assume that a travel agent claims that the average number of clients coming into the office in an
hour has a Poisson distribution with a mean of 5. Test this hypothesis with a 5% significance level if the
following occur:
(i) 2 clients in an hour. (1)
(ii) 4 clients in 2 hours.(1)
(iii) 24 clients in 12 hours.(2)
b. A human resources director states that 80% of our employees are capable of being trained for a
higher level job. A test is given to qualify a randomly picked sample of 200. According to the test 149 of
the employees are ready for additional training.
(i) Is the human resources director wrong? (A yes or no without supporting calculations gets you
nowhere. Do not use a test ratio in this section.) (2)
(ii) Find a p-value for the null hypothesis. (2)
(iii) (Extra Credit – hard) Find a power curve for this test or, at least find the power for a few
values of the population proportion. (2+++)
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