Statistics 4220 Final
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. The minutes total 100.
For this test you may use two pages of notes, a calculator, z-tables, t-table, χ2-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 “Shake it Off” during the test.
1) (5 minutes)
A paratrooper is about to jump off an airplane and parachute behind enemy lines for a top
secret mission vital to nation security. Ten minutes before jump time his pack is shot by a bullet,
and he is given a reserve parachute (which he didn’t pack himself). He assumes the pack is
good and that he will be safe. He spends the ten minutes checking it to see if he can find any
flaws so he can decide whether he should jump with it or not. He decides to not use α=0.05.
What alpha do you recommend he use, and why?
2) (5 minutes)
The distribution of depths for a “deep water” well in America is N(100, 152) feet. In Africa it is
assumed that the distribution will be the same, except the water table is lower (meaning they
have to dig deeper to find the “deep water” source). To find out how much deeper a random
sample of 20 “deep water” wells is taken, and the average is 160 feet. Find a 98.5% confidence
interval for the average depth of a “deep water” well in Africa.
3) (6 minutes)
A researcher wanted to examine the average wireless signal in the AG building at UW. He
randomly selected 40 locations in the building and noted the wireless signal strength. His 99%
confidence interval for the average signal strength in the AG building was (12, 15) dBm (which
are units that wireless signal is measured in. I googled it.)
Which of the following are valid statements (mark all that apply)
The average signal strength fluctuates between 12 and 15 dBm
The true average signal strength is between 12 and 15 dBm with 99% probability
We can be 99% confident the average signal strength is between 12 and 15 dBm
99% of the locations in the AG building have a signal strength between 12 and 15 dBm
Confidence intervals done this way capture the true average 99% of the time
There is a 0 or 1 probability that the next confidence interval would capture the true average
4) (6 minutes)
A study took 500 cell phones and dropped them in water. Afterwards some were put in a bag of
rice, others were placed in a sunny window, while others were left to dry on their own. After 24
hours whether each cell phone still functioned was examined. The data is shown in the table
below.
Bag of Rice
Sunny Window
Left Alone
Functioned
150
15
14
179
Did not function
30
15
18
63
180
30
32
242
Under the assumption of independence (that it does not matter which of the three methods is used)
explain which observed value is the most unusual and how you determined that it was unusual.
5) (4 minutes)
Last semester a Stat 3050 student wrote this on their final project:
A regression analysis on temperature verses stress level found an R2 of 0.90. That means that
90% of the temperatures can be explained by stress level
This is wrong. Rewrite the portion underlined so that their sentence is correct.
A regression analysis on temperature verses stress level found an R2 of 0.90. That means that
90% of ______________________________________________________________________
6) (5 minutes)
A random sample of 40 engineering faculty members found that 8 of them use Linux. Find a
95% confidence interval for the proportion of engineering faculty members that use Linux.
7) (12 minutes)
The new OSHA laws require mechanical engineers to video document the welding of the frame
on a Hyundai vehicle. While this may cause things to be safer, the question is whether this
significantly increases the construction time. To find out they select 12 auto technicians and
time how long it takes them to weld a Hyundai frame without video documentation, and then
how long it takes them to weld a frame with video documentation. Based on the results below
(and assuming normality) test whether the video documentation increases construction time.
With video documentation
Without video documentation
N= 12
N = 12
Average = 10.29
Average = 10.21 minutes
Standard deviation = 1.6 minutes
Standard deviation = 0.8 minutes
Pooled Standard Deviation: 1.2 minutes
Matched Pairs Standard Deviation: 0.2 minutes
8) (16 minutes)
The X-men are doing a hypothesis test of whether the number of meteors falling to Earth each
week has increased from the 15 it was in the past. They set up the following hypothesis test:
n=25 randomly chosen weeks
Assume σ = 2.5 meteors
Assume normality
H0: µ ≤ 15
Ha: µ > 15
α = 0.02
Now Green Lantern says the average is no longer 15, it’s now 16.5 meteors per week. From
Green Lantern’s perspective what is the X-men’s power?
9) (8 minutes)
In sword making it is a common myth that “quenching” the sword (to cool it down after
smelting) is best done by stabbing someone with it (blame Hollywood). It is hoped that
engineers are smart enough to know that is actually a really bad idea. A survey was done on 100
engineers and 250 non-engineers asking them whether they thought that quenching a sword by
stabbing someone with it is a good sword making technique. Find a 99% confidence interval for
the difference in proportions between the two groups.
Engineers Non-Engineers
Good idea
16
155
171
Bad idea
84
95
179
100
250
350




171
171
1  171
1  171
350
350 
350
350  0.0378
350
350




16
155
1  16
1  155
100
100 
250
250  0.0478
100
250




171
171
1  171
1  171
350
350 
350
350  0.059
100
250


171
1  171
350
350  0.0267
350
10) (16 minutes)
Three types of metal were used to fill cavities in teeth. After ten years the researchers checked
which fillings had lasted. The data is shown below. Test (with all 7 steps) whether the type of
metal matters as to whether the filling will last ten years.
Gold
Silver
Bronze
39 lasted
33 lasted
27 lasted
9 did not last
15 did not last
21 did not last
48 fillings total
48 fillings total
48 fillings total
11) (16 minutes)
A study examined the number of hours per week that civil, mechanical, and architectural
engineers worked. The data is shown below. Test (show all 7 steps) whether the data supports
that the three types of engineers work the same number of hours per week on average.
Assume the variances are equal across the groups.
Civil
n=45
x =42
s=7
Mechanical
n=40
x =41
s=6
Architectural
n=55
x =39
s=5
Overall average across all three is 40.54
The pooled standard deviation is 5.98
Matched pairs standard deviation is 2.93
The p-value for the test is 0.0398
12) (1 minute)
Out of all the classes you have taken at UW, which class would say has been the hardest so far?