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 “My Heart will go on” song in the middle of the test
In fact no one wants to hear it anymore ever
(1) (5 minutes)
The Department of Agriculture is checking the gas pumps to see if their average is below what the pump
says. The distribution is normal with a standard deviation of 0.03 gallons. He pumps gas into a tank
until the pump reads exactly 10 gallons. He does this for 3 different tanks. Then he takes them to the
lab and measures how much gas is actually in them. The average of his three tanks is 9.98 gallons.
Shade in what the p-value would look like for this test. Include all four numbers (in bold) on the graph.
(2) (6 minutes)
A test examined how much faster a tractor is than a riding lawnmower in a quarter mile race. Assume
the race time in seconds will have the same standard deviation for each machine. We borrow 36
tractors and 36 riding lawnmowers, and race them.
Find a 98% Confidence Interval for the difference in race times.
Tractor: n=36, x =16.5, s=4.6 (in seconds)
Lawnmower: n=36, x =25.7, s=7.9 (in seconds)
Pooled Variance: 41.785
Matched Pairs Variance: 11.42
Difference in Variance: 41.25
(3) (6 minutes)
The amount of voltage from a defibrillator has a known standard deviation of 250 volts. A random
sample of 16 defibrillators had an average voltage level of 700 volts. Find a 90% confidence interval for
the true average amount of volts from a defibrillator.
(4) (10 minutes)
The following data show the years before promotion for three types of engineers. The promotion times
are normal with variance 0.1792. Below is a summary, along with some calculations. Assume all
assumptions are met.
Column
n Mean Std. Dev
Chemical
5 4.740 0.342928
Civil
3 3.167 0.606446
5  4.740   3  3.167   4  5.375 
 4.558
12
Mechanical 4 5.375 0.368273
5  4.74  4.558   3  3.167  4.558   4  5.375  4.558   8.6402
2
2
2
Calculate the test statistic for testing if the type of engineer is independent of the promotion time.
(5) (8 minutes) Markie wants to estimate the proportion of her email that is actually spam using
an 80% confidence interval. For other people she knows it’s about 30%. She wants her interval
to be at most 0.02 in width. How many emails does she need to go through for her sample?
(6) (8 minutes) Emma studied 200 W shape beams, and noted the beam color and the fire
resistance (measured in hours resistance categories). She calculated the expected and partial chisquared tables, and started a test just like she learned in stat class. Then just for fun she deleted
two entries on the table. Finish her hypothesis test.
OBS
Brown
Blue
Green
2 Hours
25
29
21
75
18
15
32
65
16
20
24
60
5 Hours
7 Hours
59
64
77
200
H0: Beam color and fire resistance are
HA: Beam color and fire resistance are
α = 0.05
Exp
Brown
Blue
Green
2 Hours
22.1
17.7
19.2
23.1
7 Hours
28.8
19.1
20.8
25.0
Partial
Chi^2
2 Hours
Brown
Blue
Green
0.37
0.07
1.62
1.94
0.16
0.03
0.03
5 Hours
5 Hours
7 Hours
2.15
χ2 =
< P-value <
Therefore Fail to Reject the null
Which means there is not sufficient evidence to prove that beam color and fire
resistance are
(7) (4 minutes) The following confidence intervals were made for the difference in cell phone call times
for men verses women.
90% CI: (2.91, 22.65)
92% CI: (2.28, 23.28)
94% CI: (1.98, 23.58)
96% CI: (0.78, 24.78)
98% CI: (-2.7, 28.24)
What would the p-value be for a test of whether men and women have different cell phone call times?
(8) (12 minutes)
I was playing Candyland with my daughter and I noticed the following from 82 random observations:
My
daughter
Me
Double Cards 18
20
38
Single Cards
14
30
44
32
50
82
I’m starting to think she cheats. Test whether there is evidence that my daughter is cheating to get an
unfair portion of double cards. (math errors or calculator errors will not count against you)
(9) (7 minutes) Do Skittles give you more energy than M&M’s? To test this we ask 4 people to
eat Skittles and 4 people to eat M&M’s, and then each of them runs a mile. The next day we ask
the same runners to switch to the other candy and run a mile. Assume the sample is random and
the data is normally distributed.
Form a 98% confidence interval for the difference in means.
Skittles
N=8
Mean = 14
Std dev = 6.83
M&M’s
N=8
Mean = 15
Std dev = 8.603
Pooled Standard Deviation = 7.77
Matched Pairs Standard Deviation = 1.22
(10) (10 minutes) Do heavier cars carry just as much Freon? To answer this, Grant randomly
selected seven cars. He collected their weight and the level of Freon for each car. From a
scatterplot made with the data, regression seemed appropriate. The following output was
obtained from SPSS (where SE stands for “the Standard Error of”)
R2 = 0.348 β0 = 0.439 SE(β0) = 2.675 β1 = -1.02 SE(β1) = 0.246
Test whether heavier cars carry the same amount of Freon.
(11) (6 minutes)
When you got ready for this test you probably wondered if the batteries in your calculator needed to be
changed. If you randomly selected 100 calculators and tested how long they lasted you could know if
the average lifetime is shorter than 2 hours. Assume that if the average is significantly less than 2 hours
you will buy new batteries. What level of significance would you use and WHY?
(12) (5 minutes) The FBI determined the true average time between felony acts in the US with a 95%
confidence interval of (2.3, 5.7) seconds. Which of the following (if any) are correct?
______ 95% of the time confidence intervals like this capture the true average time between a felony
______ 95% of all felonies happen in 2.3 seconds to 5.7 seconds
______ 95% of the time the true average will be between 2.3 and 5.7 seconds
______ We are 95% confident the true average is between 2.3 and 5.7 seconds
______ There is a 95% probability that the true average is between 2.3 and 5.7 seconds
______ A new confidence interval has a 95% probability of capturing the sample average
(13) (12 minutes) The reading on a spring scale is supposed to be exact, but as it gets older the springs
stretch and it will overestimate the weight. It is safe to assume the error will be random and normally
distributed. To test an old scale an engineering company gets a weight that is exactly 2 pounds (exact to
twelve decimal places anyway). If the absolute value of the error is significantly more than 1 pound on
average then the spring scale needs to be replaced. They weigh it 4 times and get the following
measurements: 3.9, 3.02, 3.98, and 4.46. Test whether the scale needs to be replaced.
(you will need to show how to calculate the proper statistics including the standard deviation of 0.6)
(14) (1 minute)
What advice would you give to next semester? (they will see your answers at the beginning of class)