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
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 a fire alarm sound going off during the test.
1) (3 minutes) A survey in Laramie looked at college students and non college students and how many
traffic violations each had. A 90% confidence interval for the average difference between the
groups was (-1.47, 5.83). Which of the following (if any) would be statistically correct wording?
The probability that this confidence interval captured the true average difference is 0 or 1
90% of all confidence intervals done this way would correctly capture the true average difference
We cannot show with 90% confidence that the true averages are statistically different
The true average difference is between -1.47 and 5.83 90% of the time
We are 90% confident the true average difference is between -1.47 and 5.83
There’s a 90% probability the next confidence interval captures the true average difference
2) (8 minutes) Does long term exposure to sun harm bricks? To answer this engineers visited 49
buildings and measured the hardness of the bricks outside (facing the sun) and the bricks inside
(away from the sunlight). Based on the findings below test whether the sunlight lowers the
hardness of the bricks. Assume both distributions are normal and that bricks were selected
randomly.
Bricks in the sunlight
Bricks not in the sunlight
n=49
n=49
x = 37.77
x = 38.44
s = 8.41
s=8.44
Pooled standard deviation = 8.425
Matched pairs deviation = 2.39
3) (4 minutes) Last semester of the 200 students in STAT2050 there were 142 that finished early. Find
an 88% confidence interval for the proportion of students who finished early.
4) (4 minutes) They say half the people born are male, but I’d like to get a 99% confidence interval to
narrow down exactly what the true proportion is, and I’d like the interval to have a margin of error
of only half a percent. How many people am I going to need to survey?
5) (7 minutes) We have just received a report from Cowboy L00 that CSU is testing the average
temperature before a student stays home from classes. We want that hypothesis test.
Unfortunately the only thing L00 managed to sneak out of Fort Collins was the picture of their
hypothesis test as shown below. Reconstruct all 7 steps as best you can.
6) (3 minutes) Full time civil engineers are expected to work 40 hours a week. That may not match
what happens in real life. A survey of 18 random civil engineers from all over the US found an
average of 64 hours with a standard deviation of 36 hours. Find an 80% confidence interval for the
true average amount number of hours an engineer works per week.
7) (5 minutes) We assume the distribution of weights for railroad ties is normal, but we have no idea
what the standard deviation is supposed to be. We randomly sampled 10 railroad ties and got an
average of 150 lbs with a sample standard deviation of 25 lbs. Find a 96% confidence interval for
the average.
8) (10 minutes) The police are very frustrated with the intersection at the corner of Jefferson and
Pierce streets. They have noticed nearly half the people there run the light. They want to know if
the time of day changes how likely people are to run the light. They sample cars in the middle of the
day, and in the middle of the night. Test the data shown below to answer their question.
Ran light
Stopped
Day
22
18
Night
16
30
9) (6 minutes) A study found 100 engineers who had children that also became engineers. After
adjusting for inflation they compared the starting salary of the parent to the child. The regression
output for the study is shown below.
Regression Statistics
Multiple R
0.714812
R Square
0.510956
Standard Error
15.30323
Observations
ANOVA
Regression
100
df
SS
MS
F
P
102.3909
6.68E-17
1
23978.81
23978.81
Residual
98
22950.52
234.189
Total
99
46929.33
Coefficients
Std Error
t Stat
P-value
Intercept
2.670427
9.152379
0.291774
0.771076
Parent
1.183646
0.116974
10.11884
6.68E-17
Find a 95% confidence interval for the slope.
Interpret your answer using the numbers you found, the 95%, and the problem in context.
(Bonus! This question was judged “too hard for a final” by my peers. It’s worth 5 bonus points)
I had an ANOVA table written on my board with the numbers written on post-it notes. The janitor
came in last night and cleaned the board and put the post-it notes on my desk! Now I have no idea
which number went where except I’m pretty sure the F-value was 3. The numbers were:
2, 3, 4, 6, 15, 19, 24, 30, 54
Fix my table please
DF
SS
MS
F
Groups
Error
Total