Statistics 4220 Final
Version A
NAME: _________________________________________
Instructions:
Read these instructions
Do not turn the page until the test begins
You have 120 minutes
This test is printed on both sides, so don’t miss a page.
Each question is worth the number of minutes. This test is timed for 100 minutes.
For this test you may use a page of notes, a calculator, z/t/X2-tables
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.
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 “The Meow Mix” song in the middle of the test
1) (3 minutes)
A regression model was run, and the following output from the computer is shown.
Regression Statistics
Multiple R
0.85251
R Square
0.726774
Standard Error
4.119785
Observations
10
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
1
8
9
SS
361.1738
135.781
496.9548
MS
361.1738
16.97263
F
21.27978
Coefficients
5.081084
2.092335
Error
2.814349
0.453573
t Stat
1.805421
4.613001
P-value
0.108649
0.001726
P-value
0.001726
The scientist is most interested at what happens when x=6. Give the expected value at x=6.
2) (10 minutes)
The Grinch wants to know if the color of a house is related to how valuable the stuff inside it is. To find
out the Grinch gathers the following data (The scale is in thousands of dollars. That keeps the numbers
from being super huge while still allowing the Grinch to be shockingly greedy)
Color
Brown
Red
Green
Number
pillaged
17
22
8
Average
worth
15.21
17.32
13.59
Standard error
(unpooled)
4.02
4.20
3.81
Assuming that the houses of different colors should have the same standard deviation, fill in the missing
values of the ANOVA table for the Grinch.
(Hint, the total average is 15.92 and the pooled standard deviation is 4.075)
ANOVA
Group
Residual
Total
df
SS
46 825.74
MS
F
P-value
0.06771
3) (5 minutes)
Based on the p-value>0.05 in the ANOVA table above, the Grinch decides that the color of a house is
related to how much the stuff inside is worth, and consequently he is going to target red houses. Then
the Christmas Angel appears and declares that house color and the house’s value are independent.
Has the Grinch made an error, and if so, then what type of error?
5) (1 minute) Christi was asked to make a 95% confidence interval the average length of a ferret. She was
told that 150 ferrets were measured, and was given the average and standard deviation. After she
calculated her confidence interval she discovered that the average actually came from 250 ferrets. Explain
how this new information will change her confidence interval.
6) (3 minutes)
Kyle wants to test whether Republicans spend as much campaign money as Democrats
with an α=0.05. He accidentally asked Ryne to give him some confidence intervals.
Now with Ryne’s confidence intervals, Kyle wants to know whether he should reject or
fail to reject the null. Explain what he can conclude and why.
(Units are the Democrats - Republicans)
98% CI: [0.049, 0.090]
96% CI: [0.051, 0.088]
94% CI: [0.053, 0.086]
92% CI: [0.054, 0.085]
8) (8 minutes)
The Daily Stat Fact reports that over 10% of new veterinarians go bankrupt within a year. Ricky thinks the
report is way off. He gets the bank records of 625 veterinarians and finds that 49 of them went bankrupt
within a year. Test whether the percentage reported really is too high
(use a proper hypothesis test with all the steps).
12) (20 minutes)
James Bond is hired to bring Santa in for questioning. He needs to know the average weight of Santa’s
toy-bag (in kilotons). James does some research and finds three instances where Santa’s toy-bag was
measured.
Measurement 1: 23 kilotons
Measurement 2: 12 kilotons
Measurement 3: 18 kilotons
If these measurements are random and normally distributed, test whether the bag will weigh more than
10 kilotons. Show all the steps of the hypothesis test
You need to show how you calculate the standard deviation. Even if you don’t get 5.5 you can at least get partial
credit.
13) (9 minutes)
Clark is writing an article in the Daily Globe where he claims that the proportion of superheroes who get
those powers from gamma radiation is more than 2%. To test this claim Clark surveyed 200 superheroes,
and found that 5 of them were gamma irradiated.
Clark then computed his Z statistic as
z
 5200 .02
.02 * (1.02)
200
.505
and his p-value was .013
Based on this Clark decided to reject his null hypothesis.
Later Clark found out from Truthman that the actual proportion is 4%.
Did Clark make an error, and if so, then what type of error was it?
14) (5 minutes)
Given the following Anova table for a regression problem, fill in the missing values.
ANOVA
Regression
Residual
Total
df
30
SS
220
243
MS
F
P-value
0.09845
15) Suppose we are looking at the relationship between major and gender. If we rejected the null
hypothesis, which of the following would be a correct decision? Mark all that apply
______ Major and gender are related
______ Major and gender are independent
______ The distribution of majors is not the same for males and females
______ The distribution of majors is the same for males and females
16) (2 minutes) Which test is more powerful, the independent two sample test of a difference in means,
or the matched pairs two sample test for a difference in means? Explain why.
18) (3 minutes) Markie is doing a study on Airedale dogs by recording their height versus their
weight. Below is the residual plot from her regression model. Which assumptions required for
regression do you think Markie might need to check before making conclusions based on her
model, and why?
19) (5
minutes) Kyle thinks the amount of money a poultry farm spends on heating has a
relationship to their veterinary bill. He samples 81 different chicken farms, and does a linear
regression model. Fill in the ANOVA table for Kyle’s data.
Y = Veterinary bill
X = Heating bill
Regression equation:
Y = 1200 + 1.24*X
SSR=6.40
SSE=117.45
20) (5 mintues) The value of a horse is determined by its age.
After surveying many
horses and checking that the assumptions for regression were met, the following
regression equation was determined:
Value of a horse = 8000 - 200*age
Which horse listed below is the best value? Show your work
Horse
Red Fury
Light Knight
Twigger
Pastey Beauty
Age
2
9
15
25
Price
$8000
$4000
$2900
$1000
22) (5
minutes) Kayanne is growing four different kinds of peppers, but they are difficult to tell
apart when they are very young. Kayanne suspects each type of pepper attracts different bugs.
She studies 150 pepper plants and notes which insect she finds most on the plant. Her ChiSquared tables are shown below. Some of the results to test whether there is a relationship
between type of bug and type of pepper plant are shown (all math is accurate). Finish the test.
OBS
Jalapeño
Ladybug
Spider
Mosquito
6
7
6
6
25
6
8
7
5
26
6
6
4
6
22
Banana
Bell
Cayenne
Ant
8 26
7 28
9 26
3 20
27 100
H0: Pepper type and insect type are
independant
EXP
Jalapeño
Banana
Bell
Cayenne
CHI2
Jalapeño
HA: Pepper type depends on insect type
Banana
α = 0.05
Cayenne
Bell
Ladybug
Spider
Mosquito
Ant
6.5
7.0
6.5
5.0
25
6.7
7.2
6.7
5.2
26
5.7
6.1
5.7
4.4
22
Ladybug
Spider
Mosquito
Ant
0.03
0.00
0.03
0.20
0.08
0.07
0.01
0.01
0.01
0.01
0.51
0.58
0.13
0.04
0.55
1.06
7.0 26
7.5 28
7.0 26
5.4 20
27 100
3.32
χ29 = 3.32
23(8 minutes) Thomas knows horses live longer than pigs, so he doesn’t need to test it, but he does
want a 99% confidence interval for how much longer they live. Assume the variances for both groups
are not the same. A random sample of each type of animal is shown below. Calculate the 99%
confidence interval.
Horses:
Sample size: 81 horses
Sample average: 15 years
Sample standard deviation: 3.5 years
Pigs:
Sample size: 81 pigs
Sample average: 12 years
Sample standard deviation: 1.2 years
Pooled variance: 6.93
Matched Pairs variance: 2.82
Weighted variance: 5.52
25) (10 minutes) A university is concerned that it is taking students too long to complete their requirements and
graduate; the average time for all students is 4.7 years. The dean of the honors program takes a sample of 32
students and finds that the average amount of time it takes honors students to graduate is 4.5 years with a
standard deviation of 0.5 years. Test the dean’s claim that the amount of time it takes for honors students to
graduate is less than 4.7 years at the .05 level of significance.
27) (8 minutes) “What is the fastest you have ever driven a car (mph)?”
Males: n = 7, 𝑥̅ = 107.4 mph, and s = 17.4 mph
Females: n = 5, 𝑥̅ = 88.4 mph, and s = 14.4 mph
Matched Pairs standard deviation = 12.1 mph
Assuming that this represents a random sample from a normal distribution, find a 95% confidence interval for
the difference in average fastest speed driven by men verses driven by women.
28) (15 minutes) Two engineers are arguing about the average strength of a 2x4 made of titanium. They are
planning a test using 9 titanium boards where they will increase the force on the beam until it snaps. Bill says it
will take an average of 50 KPSI. Will says it will take 70 KPSI. They find on Wikipedia that the distribution is
normal with a standard deviation of 21 KPSI. Bill is going to do the test with α=0.05 (which means he will
assume he is right until proven otherwise). Will wants to know what the power of Bill’s test is for his estimate of
the average. Find the power.
29) (12 minutes) The Jolly Rancher factory has five different machines producing the five flavors of Jolly
Ranchers. The Mixed Bag is supposed to have the following distribution for each type (when the machine is
working properly)
Watermelon
18%
Green Apple
18%
Lemon
20%
Cherry
22%
Peach
22%
The quality control expert randomly samples 1000 jolly ranchers and gets the following counts
Watermelon
170
Green Apple
200
Lemon
190
Cherry
190
Does he have evidence that the machine is not working properly?
Peach
250