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) (4 minutes)
The following output is from a regression model using Excel to predict the temperature of Top
Raman based on the length of time in the microwave. Lengths ranged from 10 seconds to 500
seconds. The residual plot did not show any potential problems. Based on the output, if I nuke
my Top Ramen for 120 seconds, how hot should it be?
SUMMARY OUTPUT
Regression Statistics
Multiple R
1
R Square
1
Adjusted R
Square
1
Standard Error
0.104683
Observations
23
ANOVA
df
Regression
Residual
Total
Intercept
Seconds
1
21
22
Coefficients
60
1.1
SS
MS
F
765310.3 765310.3 69837094
0.230129 0.010959
765310.5
Standard
Error
t Stat
0.043402 1382.424
0.000132 8333.333
P-value
1.46E-53
5.7E-70
Significance
F
5.7E-70
Upper
Lower 95%
95%
59.90944 60.08996
1.099716 1.100263
2) (6 minutes)
A 90% confidence interval for the average distance that a nail gun will shoot is (45, 68) yards.
Which of the following statements is a valid way to talk about this interval? Select all that apply
The probability that a new interval would capture the true mean is either 0 or 1.
There is a 90% probability that a new confidence interval would be (45, 68)
The true mean is either between 45 and 68 or it is not.
We are confident the mean is between 45 and 68 by using a method that is correct 90% of the time.
The true average is between 45 and 68 about 90% of the time
The true average distance is between 45 and 68 yards with 90% confidence
3) (10 minutes)
There is talk of a new biomimetic plating that could be used to coat wires and would make a
wire signal faster. To test it we found 12 different types of wires (from triplex wire to copper
wiring, to gold wiring, and even ear phones). Then we cut each wire in half and coated one of
the halves in biomimetic plating. We tested the speed of an electrical signal through each half
of each wire. Find a 99% confidence interval for the average difference between the normal and
the biomimetic plated wires assuming normality.
Normal wire:
12 wires
Average of 0.46c
Standard deviation of 0.08c
Biomimetic plated wire
12 wires
Average of 0.82c
Standard deviation of 0.11c
Pooled Standard Deviation: 0.095c
Matched Pairs Standard Deviation: 0.02c
Two Sample Independent Sum of Deviations: 0.19c
4) (5 minutes)
I needed a 95% confidence interval for the average age of a house in Laramie. I randomly
selected 100 homes in Laramie and I found an average age of 25 years with a standard deviation
of 8 years. What is my confidence interval?
5) (6 minutes)
The distribution of the amount of money a college student spends on their computer (including
hardware, software, and online subscriptions) during their freshman year is normally distributed
with a standard deviation of $700. I want an 88% confidence interval for the mean that has a
margin of error no less than $35.50. How many college freshmen will I need in my study?
6) (6 minutes)
Walmart wants to test whether the average weight a paper bag can hold is less than the average
weight a plastic bag can hold. To find out they randomly selected 20 paper bags and 20 plastic
bags and measured how much weight the bag could hold before it broke. Based on the data
below test whether the paper bags hold less than plastic bags.
Paper bags
N=25
x = 20 lbs
S = 10 lbs
Plastic bags
N=25
x = 30 lbs
S = 20 lbs
Pooled standard deviation: 15.8
Matched pairs standard deviation: 5
7) A regression analysis examined the relationship between the age of a person with an iPad and
the time before the iPad is dropped and broken in months. The output is shown below.
Residuals Versus ages
(response is time)
20
Residual
10
0
-10
-20
0
10
20
30
40
ages
50
60
70
80
time = - 1.28 + 0.137 ages
Predictor
Constant
ages
S = 8.39116
Coef
-1.277
0.13713
SE Coef
4.228
0.06778
R-Sq = 4.0%
Analysis of Variance
Source
DF
SS
Regression
1
288.19
Residual Error 98 6900.33
Total
99 7188.53
T
-0.30
2.02
P
0.763
0.046
R-Sq(adj) = 3.0%
MS
288.19
70.41
F
4.09
P
0.046
a)
(3 minutes) Based on the output above, which of the 5 assumptions for regression are most
worrisome, and why do you think it could be a problem?
b)
(6 minutes) Test (with a full hypothesis test) whether there is a relationship between the age
and the time before a person drops their iPad. The first three steps are done to help you.
H0: β1 = 0
Ha: β2 ≠ 0
α = 0.05
8) (10 minutes)
CSU claims that the salaries of their engineering graduates are just the same as salaries for UW
graduates. They claim they should have the same mean and the same standard deviation. The
engineering department here is skeptical, and they want to test if the means are actually
different. They find 64 CSU engineering graduates have an average salary of 55K with a
standard deviation of 20K. They find 38 UW engineering graduates have an average salary of
62K with a standard deviation of 10K. Test whether CSU’s claim of equal averages is false.
H0: µCSU = µUW
Ha: µCSU ≠ µUW
α = 0.05

55  62  0
t

64

38
9) (1 minute) If statistician wanted to take an epic selfie, how could they do it?