Statistics 4220 Test 2
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 a page 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 “Oh the weather outside is beautiful” during the test.
Your boss has never taken statistics. He has data on the heat transfer rate of a refrigerator coil (J/m) as
it relates to the length of the coil (in cm). Your coworkers have examined 200 refrigerator coils of
different lengths, and the heat transfer rate of the coil. Your boss is now interested in knowing: “If I
lengthen the coil by one centimeter, how much will the heat transfer rate change?”
The output from the regression analysis is shown below.
Residual standard error: 16.49
Sample size: 200
Multiple R-squared: 0.05013
Adjusted R-squared: 0.04533
(Intercept)
Coil Length
Estimate Std. Error
t
P
-1.53927 2.86769 -0.537 0.59203
0.18785 0.05811 3.233 0.00144
(4 minutes)
Find a 90% confidence interval for the slope of the regression line.
(2 minutes)
Use one sentence to report back to your boss what the confidence interval you found above means.
Include your answer above, the 90%, and the refrigerator coil.
(3 minutes)
A study surveyed the batteries in the calculators of 150 randomly selected engineers to determine the
average battery capacity (measured in mAh). The 80% confidence interval was (92, 114) mAh.
Which of the following sentences is statistically correct?
A) 80% of the 150 engineers had battery power between 92 and 114 mAh
B) The true average battery power is between 92 and 114 mAh with 80% confidence
C) There is an 80% probability that the true average battery power is between 92 and 114 mAh
D) 80% of the time that a study like this is done the true average will be between 92 and 114 mAh
E) The next confidence interval has an 80% probability of being (92, 114) mAh on average
(8 minutes)
A new graphics processor is supposed to be installed next to the motherboard of the Smarterphone5.
However, if the average heat from the processor is 80° or more then it will cause the motherboard to
fail before the warranty runs out. A team is organized test if the processor is safe to use at the 1%
significance level. They have deduced the standard deviation is only 2°. They plan to randomly select 36
processors to test. If the true average is actually 79°, then how powerful is their test be?
(5 minutes)
In championship chess the amount of time it takes a person to make a move is random with a standard
deviation of 35 seconds. Dr Kcops wants to estimate the average with 93% confidence, and he wants a
confidence interval that has a margin of error that is less than 10 seconds. How many random chess
moves does Dr Kcops need to sample?
(5 minutes)
You’ve been asked to check whether the inventory amounts listed by the supply supervisor match the
actual amounts you can count in the stockroom. If they do not match that indicates the supervisor is
stealing supplies and then “cooking the books” to hide it. Of course sometimes counts are off, and
sometimes stuff gets misplaced, so you decide to randomly select 31 inventory items and check your
count with the listed amount. If the list and the actual amounts are significantly off then you will accuse
the supervisor of theft.
Choose what α you would use and explain why you chose it.
(3 minutes)
A random sample of 16 people found that 50% of them love chocolate. Find a 95% confidence interval
for the proportion of people who love chocolate.
(9 minutes)
The police are expected to let 10% of the people they pull over go with only a warning. Officer Callison
is known to be ruthless, and his commanding officer suspects he is not letting enough people go with a
warning. She randomly selects 85 records from Officer Callison and finds that 17 of them got off with a
warning. Test whether Officer Callison is not letting enough people get off with a warning.
(10 minutes)
Assume the distribution of test taking times is normally distributed. For the first draft of this test I tried
to make it 50 minutes on average. I asked 4 friends to take the test and timed how long they took.
Their times are listed below. Assuming that these friends are a good way to measure how long a 4220
student needs, test whether this first draft was 50 minutes on average.
Hint: first you’ll need a mean and standard deviation
Elena: 61.5 minutes
Alaric: 73.5 minutes
Stefan: 51.5 minutes
Damon: 49.5 minutes
(1 minute)
If a statistician and an engineer got into a fight, who would win and why?