Statistics 101
Final Exam
May 10, 2002
Name:
ID#
INSTRUCTIONS: Read the questions carefully and completely. Answer each question and show
work in the space provided. Partial credit will not be given if work is not shown. When asked to
explain, describe, or comment, do so within the context of the problem.
1. [6 pts] The usual interpretation of a 90% confidence interval for the population mean has
two parts:
• Reasonable or acceptable values for the population mean.
• 90% of intervals will capture the population mean.
Draw pictures that illustrate each part of the interpretation of a 90% confidence interval for
the population mean. Be sure to clearly indicate which picture illustrates the 90% capture
rate and which picture illustrates the acceptable values.
2. [4 pts] What does the Central Limit Theorem tell us?
1
3. [15 pts] Pollution from automobiles is a major concern, especially in high population density
areas. The EPA conducted a study to see if there was a relationship between mileage on a
car and carbon monoxide (CO) emissions. Below are the data. Also refer to the JMP output
provided on page 3.
Mileage
CO Rate
1000
56
2200
58
3000
60
4000
75
5300
77
6000
86
7000
93
8100
98
(a) [2] What is the explanatory variable? What is the response variable?
(b) [2] From the JMP output, give the least squares equation relating CO Rate to Mileage.
(c) [3] Give an interpretation of the intercept within the context of the problem.
(d) [3] Give an interpretation of the slope within the context of the problem.
(e) [3] Use the least squares equation to predict the CO Rate and calculate the residual for
the car at 6000 miles.
(f) [2] What is the correlation between CO Rate and Mileage?
2
Bivariate Fit of CORate By Mileage
100
90
CO 80
R
a
t
70
e
60
50
0
2000
4000
6000
Mileage
8000
10000
Linear Fit
Linear Fit
Pred CORate = 45.620382 + 0.0065037 Mileage
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
0.961491
0.955073
3.447539
75.375
8
Parameter Estimates
Term
Intercept
Mileage
Estimate
45.620382
0.0065037
Std Error
2.719459
0.000531
t Ratio
16.78
12.24
7.5
5.0
R 2.5
e
s
I 0.0
D
u -2.5
a
l
-5.0
-7.5
0
2000
4000
6000
Mileage
8000
10000
3
Prob>|t|
<.0001
<.0001
4. [5 pts] The graph below shows the sampling distribution of the sample mean for samples of
size n=9.
Circle the graph which represents the population from which the samples are taken. Explain
your choice briefly.
4
5. [15 pts] Short answer.
¯
(a) [3] A study was done looking at the relationship between high school rank and first year
college grade point average. The study reported a correlation of r =1.31. What does
this value indicate?
(b) [2] Keeping all other things the same, decreasing the sample size will decrease, keep the
same, increase the margin of error.
(c) [2] Increasing the sample size will cause the center of the sampling distribution of X to
decrease, stay the same, increase.
(d) [3] The sample mean being much smaller than the sample median indicates what about
the shape of the distribution?
(e) [2] Keeping all other things the same, increasing the level of confidence will cause the
margin of error to decrease, stay the same, increase.
(f) [3] The spread of the sampling distribution of X for samples of size 36 is 10. What is
the spread of the sampling distribution of X for samples of size 16?
5
6. [5 pts] The three principles of a well designed experiment are control, randomization and
replication. Between control and randomization, which do you think is the most important?
Support your answer.
Because the final exam is one of the last exams given during finals week, final grades
will not be posted until May 14. Grades will be posted according to the last 4 digits
of your ID# outside Snedecor 101. You can look at your corrected final exam in my
office. However, I keep all final exams for one semester.
6