Statistics 4220 Final
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 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 “Let it Go” during the test.
1) (2 minutes) You see a homeless guy on the street. He could either be really homeless (in which
case you will want to give him money) or he could be a scam artist (in which case you would
NOT want to give him money).
Which hypothesis is your null hypothesis?
To find out whether to reject your null you ask him questions (like “What is your story?”).
Whether you reject or fail to reject determines whether you will give him money. State what
your personal alpha is (not 0.05) and why you like that alpha (based on which error you want to
avoid).
2) (5 minutes) A regression test is done on 50 data points. The standard deviation of the data
around the regression line was 4.596. The R2 was 0.097. Also the p-value was 0.0276 and
  yˆ  y 
2
 109
Fill in the ANOVA table
DF
SS
MS
F
P
Regression
Error
Total
3) (4 minutes) A random sample of 450 people with iphones found that 391 of them had paid to
install a game on their phone. Find a 97% confidence interval for the proportion of people with
an iphone who have paid to install a game on their phone.
4) (6 minutes) The following table examined different companies and the one-year failure rate of
their earphones. Test whether it matters what company you buy your earphones from as far as
whether they will fail after one year.
Sonny
Skullveggies Rose
Sure
Working
126
199
124
110
Failed
15
12
16
18
141
211
140
128
559
61
620
Sonny
Skullveggies Rose
Working
127.13
190.24
559
EXP
Failed
13.87
141
20.76
211
140
Sure
128
61
620
X2
Sonny
Skullveggies Rose
Sure
Working
0.01
0.403
0.039
0.253
Failed
0.092
3.696
5) (3 minutes) A one sample z-test for the mean weight of a car was done using 130 random cars.
When the data was put into the computer a 98% confidence interval for the mean was (3221,
4009) lbs. Which of the following sentences can we guarantee will always be true (if any)?
If we were testing H0: µ = 4000 the p-value would be below 0.02
If we were testing Ha: µ ≠ 4000 the p-value would be above 0.01
If we had sampled only 100 cars the confidence interval would contain the number 4000
We are 98% confident the true average mean is between 3221 and 4009
98% of the time a confidence interval like this is done it will contain the number 4000
The true average is between 3221 and 4009 lbs 98% of the time.
6) (7 minutes) A new type of bulletproof glass is being tested to see how many shots of a .70
caliber bullet the glass can take before a bullet actually can get through. The company says it
can take more than 50 shots on average before it is compromised. Four different panes of this
glass were tested. The number of .70 caliber bullets each could take is shown below. Test
whether the companies claim can be supported. Assume normality. (First you will need to show the mean is 158 then
show how to calculate the standard deviation as 90)
59, 131, 167, 275
7) (3 minutes) Seven friends work at a mine. They claim the time it takes to find a valuable gem is
the same for all seven of them on average. They keep track for the next year and compare their
data afterwards. The assumptions for ANOVA were satisfied, and the p-value they got was 0.03.
Using an α of 0.05 which of the following are valid conclusions?
The evidence shows their averages are all the same
The evidence shows their averages are all different from each other
The evidence does not show there are any averages that are different
The evidence shows at least one average is different from the others
The evidence shows there is someone who is faster than another in this group
The evidence shows there is one person who is faster than all the others
The evidence shows my kids were watching Snow White while I wrote test questions
8) (4 minutes) A test was done on shingles to see if copper shingles would work differently than
wooden shingles on a house. The number of shingles that had to be replaced in twenty years
was recorded. Based on the data shown determine whether there is a difference.
Not replaced
Were replaced
Copper Shingles
189
6
The following equations may (or may not) be helpful
189
 583
591
 1.30
189
583
1  189
1  583
195
195 
591
591
195
591

195

189
 583

591
 1.58
772
772
772
772
1
1
786
786 
786
786
195
591

195




Wooden Shingles
583
8
9) (5 minutes) We want to make a confidence interval for the proportion of UW undergrad
students who are freshmen. We need the margin of error for a 99% confidence interval to be
no more than 0.01. We really have no idea where to start (hint – this means you will need to
suggest a reasonable value as a starting parameter. Any reasonable guess for the missing
parameters you need to answer this question will be accepted). Suggest a sample size and show
how you calculated that as the value for n.
10) (5 minutes) Two methods have been proposed to predict the shear strength of a steel girder
based on the thickness. The Tidneb method and the Reppans method. To compare these two
methods 12 girders are randomly selected where each girder has a different thickness. The
predicted shear strength is calculated using each method. The summarized results are shown
below. Find a 95% confidence interval for the difference in the averages(assuming normality).
Tidneb method:
12 girders
Average: 1.32
Standard deviation: 0.06
Reppans method:
12 girders
Average: 1.65
Standard deviation: 0.05
Pooled standard deviation: 0.055
Matched Pairs Standard Deviation: 0.01
11) (5 minutes) The following output is from data that randomly selected times to measure the
number of server requests per minute and the stock market. Test whether the stock market has
an effect on the number of requests a server receives.
Server Requests = 497 + 0.0023 Stock Price
Predictor
Constant
Stock Price
S = 80.9373
Coef
496.59
0.00228
SE Coef
13.57
0.01104
R-Sq = 0.0%
Analysis of Variance
Source
DF
SS
Regression
1
279
Residual Error 998 6537746
Total
999 6538025
T
36.60
0.21
P
0.000
0.837
R-Sq(adj) = 0.0%
MS
279
6551
F
0.04
P
0.837
12) (1 minute) If you were asked to create a comic book superhero statistician, what superpowers
would you give him?