[ answers in web view ]
As an aid for your study, here are a collection of questions similar to what
might show up on the midterm exam. The actual exam may be longer or shorter,
there may be some material on the exam that is not covered here, and there may
be some material here that doesn't show up on the exam. The coverage for the
exam is ch1-8 in our textbook.
The exam is in-class, 70min long, and you will enter your answers on the
computer. You may use Excel, the lecture notes, textbook, and any resource
on the Internet that is not a live person. You may not communicate in
any way (including text message, email, chat, etc.) with classmates or anyone
outside of class; if you have a question, raise your hand and I will help you
as much as I can.
- A quality control inspector has rated each batch produced today on a scale
from A through E, where A represents the best quality and E is the worst.
What is the level of measurement of this variable?
- Your customers’ average order size is $2601, with a standard deviation of
$1275. Suppose 45 typical customers independently placed orders tomorrow.
What are the chances that tomorrow’s average order per customer will be between
$2450 and $2750?
SE=190, z = -0.7945 and +0.7839, so area in between is 57%
- Using the information in the preceding problem, produce a 95% confidence
interval on average order per customer per day, assuming 20 customers per day.
SE=285.10, z = +/- 1.96, so conf. int. is between $2042.22 and $3159.78.
- The table below shows sales of some “light” foods:
My company is planning to launch a new brand of light food. Our goal is to
reach at least the 20th percentile of current brands. What is our sales goal,
| "Light" Food|| Sales ($Millions)|
|Entenmann's Fat Free baked goods || $125.5 |
|Healthy Request soup || $123.0 |
|Kraft Free processed cheese || $83.4 |
|Aunt Jemima Lite and Butter Lite pancake syrup || $58.0 |
|Fat Free Fig Newtons || $44.4 |
|Hellmann's Light mayonnaise || $38.0 |
|Louis Rich turkey bacon || $32.1 |
|Kraft Miracle Whip free || $30.3 |
|Ben & Jerry's frozen yogurt || $24.4 |
|Hostess Lights snack cakes || $19.3 |
|Perdue chicken/turkey franks || $3.8 |
|Milky Way II candy bar || $1.1 |
rank=2.4, round up to 3: 3rd entry is $19.3.
Or, using PERCENTILE(): $20.32.
The difference is due to
the different way Excel computes percentiles.
- Produce a relative frequency histogram for the variable "Airline" in the
- Using the same dataset from the preceding problem, produce a joint
frequency distribution for the two variables, "Male/Fem." and "Business or
Pleasure". Are these two variables independent in this dataset? Why or
No: e.g., P(Business | Male) ≠ P(Business | Female)
- You have followed up on people who received your catalog mailing. You
found that 4% of these people ordered the hat, and 6% ordered the mittens. Of
the people who ordered the hat, 55% also ordered the mittens. Of the people
who did not order the hat, what percentage ordered the mittens?
Given: P(H)=4%, P(M)=6%, P(M|H)=55%,
the question is looking for P(M|noH).
Then P(M and H) = (.04)(.55) = 2.2%.
Since P(M and H) and P(M and noH) must add up to P(M), so
P(M and noH) must equal 6% - 2.2% = 3.8%.
We are looking for P(M|noH), which is P(M and noH) / P(noH).
P(noH) must be 100% - P(H) = 96%, so
P(M|noH) = 3.8% / 96% = 3.958333%.
- Here are the satisfaction scores given by 12 randomly selected customers:
Does the observed average differ significantly from the target score of 80?
|89 || 98 || 96 || 65 || 99 || 81
|| 76 || 51 || 82 || 90 || 96 || 76
mean = 83.25, SD = 14.63, SE = 4.223.
z = (80-83.25)/SE = -0.77, % area in left tail = 22.08%.
No, does not significantly differ (technically, this question is a ch9
question if we consider an α, but the components are within ch7-8).
- In a nationwide poll for a political candidate, we found that 309 out of
1105 registered voters claimed to be in favor of that candidate. If we report
our findings with 95% confidence, what is our margin of error?
SE = 1.3502%, z=1.96, so margin of error (the +/- in the confidence
interval) is just (1.96)(1.3502%) = 2.65%
- In order to pay your firm’s debts this year, you will need to be awarded
at least 2 contracts. This is not usually a problem, since the yearly average
is 5.1 contracts. What is the probability that you will not earn enough to pay
your firm’s debts this year? (Hint: which distribution is appropriate?)
POISSON(1, 5.1, 1) = 3.72%
- Your client has a particularly complex database procedure it needs to run
quickly. Your company can provide a new computer system to speed it up.
You have run the procedure on your new system 14 times (independent runs) and
obtained the following runtimes (in minutes):
You would like to claim that your new system is very fast. In your advertising,
you will say, "average processing time is as low as ___". Find the appropriate
bound of the two-sided 95% confidence interval.
5 || 8 || 5 || 6 || 11 || 9 || 8 ||
10 || 5 || 11 || 6 || 5 || 5 || 10
t-score is TINV(.05,13) = 2.16.
mean = 7.43, sd = 2.41, SE = 0.6438.
Conf int is 6.038 to 8.819 (we want the lower bound).
- You would like to estimate the average price of a stock to a precision
of +/- 1%, with 95% confidence. Assume the volatility (coefficient of
variation) of the stock is 12%. Assuming each day's price is independent
and normally distributed, how many days should you track the stock in order
to attain this precision in estimating its average price?
SD = 0.12μ, so SE = 0.12μ/sqrt(n).
Margin of error = 0.01μ.
95% confidence implies a z-score of NORMSINV(0.975) = 1.96, so
1.96 = 0.01μ / (0.12μ / sqrt(n)).
Solving for n: n = ( (1.96)(0.12)/(0.01) )2 = 554
- (p.255 #41) The mean time between failures (MTBF) for a particular model
of power supply unit (PSU) is 4,000 hours. Some PSUs may fail earlier; some
later. What is the probability of a random PSU failing in less than 2,100
hours? (Hint: which probability distribution is appropriate?)