Download Final Exam, Fall 02

Ecn. 220
Fall 2002
Todd Easton
Final Exam
Before beginning the exam, please read the following pledge and sign it. Return this sheet with your exam
answers.
I promise that I will not send or receive email, or surf the Web, during this class period. I promise that I
won’t look at other students’ monitors or exams. I promise that the only outside materials I relied upon were
my three 3 x 5” cards. I promise that the work I turn in is mine alone.
__________
Please answer each of the following questions. Show all your work (if you use Excel, type or copy each
formula). Unless a specific method of answering a question is specified, feel free to select a method of your
own choosing (e.g. paper and pencil or Excel). Please write answers only on the front of each sheet you use
and please put your name on the back of each sheet. I’d like to grade each exam without knowing the
identity of the author. If a question is about a sampling situation, assume the population size is very large,
compared to the sample, unless the question says otherwise.
1) Of employed US adults age 25 or older, 90.5% have completed high school, while 29.7% have completed
college. Suppose one is selecting from this population at random. Also, suppose that everyone who
completed college also completed high school. Given that you select that someone has completed high
school, what is the chance they also completed college?
2) You recently initiated a new marketing campaign. The goal of the campaign is for more than 25% of
supermarket shoppers to recognize your company’s brand. You just got back the results from a survey of
150 random shoppers: 28.2% recognized your brand name.
a) Suppose you are clear that the burden of proof is on you to show that, at the 5% confidence level,
the goal of the campaign has been reached. What is your null hypothesis? Please explain your
choice.
b) Perform the test of the hypothesis you selected in a). Present the result and explain it. Make the
explanation clear enough that someone who never studied statistics could understand it.
3) A machine fills 12-ounce cans. It misfills a can 0.1% of the time.
a) If a case of 24 cans is tested for proper filling, what is the probability that there is 1 incorrectly
filled can?
b) If a case of 24 cans is tested, what is the probability that there is 1 or more incorrectly filled can?
2
***************
For the fourth question on the exam, you have a choice. Please do only one of the following: 4A or 4B.
4A) Suppose you are responsible for product quality at a paper plant. You take random samples of output
during each two-hour period. For one particular two-hour period, the sample mean was 4.015 thousandths of
an inch for the 16 sheets you sampled. The sample standard deviation was .00675 thousandths of an inch.
a) Explain the meaning of the sample standard deviation number.
b) Calculate a 95% confidence interval for the population mean paper thickness.
c) Would you need to make any assumptions to calculate this interval? Please explain.
4B) Below find two regressions. Please describe the difference between the scatters of points in the two
diagrams. Please explain the difference in the strength of the two x-y relationships graphed. In your
explanation of the strength difference, please comment both on the slope coefficient estimated and on the R2.
Predicting y: Regression 1
y
300
250y = 3.9727x + 28.532
200
150
100
50
2
R = 0.6836
0
-50 0
10
20
30
40
50
60
50
60
x
Predicting y: Regression 2
y'
300
250
200
150
100
50
y = 2.5287x - 25.812
0
-50 0
2
R = 0.891
10
20
30
x
***************
40
3
5) A student of mine, Piti Tantivirasut, was interested in tourism to Thailand. He used Excel to estimate the
model given below. His dependent variable was the number of tourists arriving in Thailand in a particular
quarter (Q1=January-March, Q2=April-June, Q3=July-September, Q4=October-December) during a fouryear period. He reasoned that:
 tourism was highest during the fourth quarter, when weather was particularly good, so he
included in his model a dummy variables: Q4=1 if the arrivals are during the fourth quarter
and otherwise =0.
 there was general rise in tourism to Thailand, so he included a variable that increased by one
with each passing quarter (Time).
Figure 1, Predicting Tourism in Thailand between 1997, Q1 to 2000, Q4
Regression Statistics
Multiple R
0.899
R Square
0.808
Adjusted R Square
0.778
Standard Error
153206
Observations
16
ANOVA
df
Regression
SS
2
MS
1.28015E+12
6.4E+11
Residual
13
3.05136E+11 2.35E+10
Total
15
1.58529E+12
Coefficients Standard Error
Intercept
Q4
Time
1612380
332893
47247
80845
90057
8459
t Stat
19.94
3.70
5.59
a) Explain the meaning of the coefficients on the two variables Q4 and Time, from the results
presented in Figure 2.
b) Please use the t-statistic for Q4 to test the the null hypothesis that coefficient of Q4 in the
population regression is zero. Use an alpha of .05.
c) Interpret the result of the t-test from b). Pretend you are helping someone who knows little
statistics understand what that 3.70 means.
c) Please plot the residuals against time. Present the plot and explain what it tells you about the
validity of the model of tourist arrivals presented here. The residuals, along with the data and the
estimation, are in an Excel workbook:
Fac-Stu\Bus\Easton\Ecn. 220\FinExmData.xls