Statistics 4220 Test 2
NAME: _________________________________________
Instructions:
Read these instructions
Do not turn the page until the test begins
You have 50 minutes
This test is printed on both sides, so don’t miss a page.
Each question is worth double the number of minutes. This test is timed for 50 minutes.
For this test you may use a page of notes, a calculator, z-tables, t-table
If you need any of these please find a solution before the exam begins
If you have a question during the test please come forward quietly so that you are not
disruptive. If you leave early please do so quietly. Note that I cannot give answers that
are part of the test, only clarify the English being used.
All hypothesis tests need to show all 7 steps.
You must show your work. Answers which are correct but do not show any work may
not get full credit. I might assume you either guessed, cheated, or used some fancy
calculator.
Cheating is not tolerated. Any inappropriate activity will be discussed after the final
Hats or hoods must be moved so that your face is not obscured.
Please turn off your cell phone. You cannot have your phone out at all.
No one wants to hear “Happy” by Pharrell Williams during the test.
1) (5 minutes)
Dr. Redav wants to know the average force that it takes to destroy a 1.22 meter block of
terra rock. He assumes the distribution is normal with a standard deviation of 12.3
Newtons. His grad student, Luke, randomly selects 12 samples of 1.22 meter blocks of terra
rock. The sample average force is 113.8 meters. Find an 84% confidence interval for the
true average force required to break the terra.
2) (5 minutes)
A 95% confidence interval was made to find the average coefficient of friction for dragging
bare skin over rough wood. The confidence interval was calculated as (0.25, 0.50). Which of
the following sentences is statistically correct?
_____ There is a 95% probability that a new confidence interval would be able to correctly
capture the true average coefficient of friction.
_____ The average coefficient of friction between skin and wood is between 0.25 and 0.50
with 95% confidence.
_____ 95% of the time the average coefficient of friction between skin and wood would be
between 0.25 and 0.50.
_____ The sample average for the coefficient of friction between skin and wood from this
study must have been 0.375 because it is exactly in the middle of the interval.
_____ The probability that this confidence interval did correctly capture the true average
coefficient of friction is either zero or one.
3) (7 minutes)
Batman claims the average number of crimes in New York is more than 4,000 per day. To
test it he plans on randomly selecting 100 days and testing with α=0.01. Superman says that
number is a little low, it should be 4309.6 per day. They both agree the standard deviation
is 900 crimes per day. If Superman is right, then what would be Batman’s power?
4) (5 minutes)
The following output shows data from my 2050 class (but I won’t tell you when because it’s
against FERPA laws). The y-axis shows their score in the final. The x-axis shows their score
on exam 1.
(Intercept)
exam1
Estimate
16.47223
0.70511
Std. Error
7.85370
0.09926
t value
2.097
7.104
Pr(>|t|)
0.0374
2.9e-11
Residual standard error: 16.17
Multiple R-squared: 0.2228
Adjusted R-squared: 0.2184
N=178
a) Based on the output above, explain whether you feel like there are any assumptions
for simple linear regression that we ought to worry about, and explain why you
think those assumptions are a concern.
b) Assume the assumptions are met so you can do a 90% confidence interval on the
amount that the final score is expected to increase based on each point of exam 1.
5) (8 minutes)
Do drivers in Laramie drive better than drivers in Denver? To find out a random sample of
16 Laramie drivers and 16 Denver drivers (all of whom were 30-40 years old and drive 60 to
80 minutes per day) had the number of citations in the past 10 years reported. For the 16
Laramie drivers they had an average number of citations of 4.4 with standard deviation of
1.3. The 16 Denver drivers had an average of 5.6 citations with a standard deviation of 1.5.
The matched pairs standard deviation was 0.9. Assume normality.
Test whether the average for Laramie drivers is less than for the Denver drivers.
6) (5 minutes)
A random sample of 25 trees took each tree and cut two boards from each tree. One board
was treated with Pledge Wood Finish while the other board was treated with Gorilla Glue.
Then each board was subjected to 5 minutes of a wide-beam laser which simulates 50 years
of being in the sun. The force needed to break the board was then measured. Using the
data below test whether there is a difference in the average force to break the boards based
on whether they were treated with Pledge or Gorilla glue.
Pledge:
Twenty-five boards
x = 60 Newtons
S = 15 Newtons
Gorilla Glue:
Twenty-five boards
x = 70 Newtons
S = 20 Newtons
Matched Pairs standard deviation: 5 Newtons
7) (5 minutes)
Eigoob Nam is hired to find the average number of times a two-year old child would drop a
cell phone each day (if a parent were to give a cell-phone to their two-year old child). To
find out he plans on randomly selecting two-year old children, give them a cell phone, and
follow them around for a day. Assume the standard deviation is known to be 15.6 drops.
He needs a 95% confidence interval that will have at most a margin of error of 2.95. How
many two-year old’s will he need for his study?
8) (9 minutes)
The NSA makes their own proprietary computers by purchasing silicon ingots from two
different companies: Trid3 and Kcor Inc. Ingots from Trid3 are more expensive, but the
company says that’s because it has a different toxicity level. The NSA recently acquired an
email from Kcor Inc suggesting that the NSA is stupid to think there is any difference and
that all the ingots actually come from the same source. Now the NSA believes the standard
deviations are equal (since they supposedly come from the same place anyway).
Using the data below test whether there is a difference in the average toxicity level.
Trid3
N = 50 ingots
Average: 12.2 LD
Std dev: 2.4 LD
Kcor Inc.
N = 80 ingots
Average: 11.9
Std dev: 1.8 LD
Matched Paris standard deviation: 1.1 LD
9) (1 minute) In a zombie apocalypse, what would be the role of a statistician?