Download SOME EXTRA QUESTIONS I will try to post three new questions per

SOME EXTRA QUESTIONS
I will try to post three new questions per week - just to keep your mind active. The answers are
on the last page.
(1) A simple random sample of 1200 adult Americans is selected and each person is asked
the following question.
In light of the huge national deficit, should the government at this time spend additional
money to establish a national system of health insurance?
Only 39% of those responding answered yes. Determine whether each of the following
statements regarding this survey is true or false.
(a) This survey is reasonably accurate, because it used a large, simple random sample.
(b) This survey probably overstates the percentage of people who favour a system of
national health insurance.
(c) This survey probably understates the percentage of people who favour a system of
national health insurance.
(d) This survey is very inaccurate, but neither understates nor overstates the percentage
of people who favour a system of national health insurance. Because simple random
sampling was used, it is unbiased.
(2) Let the random variable X = the time between the moment that the CRA receives your
tax return forms and the moment you receive your tax refund. It is known that X follows a
uniform distribution over the range of 2 weeks and 10 weeks. Define the following events:
A = {It takes more than 5 weeks to receive your refund} and B = {it takes less than 8
weeks to receive your federal tax refund}. Are A and B independent? HINT: to answer
the question you will need to do some calculations.
(3) The time it takes a student to walk from the dorm to the chemistry lab follows roughly a
Normal distribution with a mean of 20 minutes and standard deviation of 3 minutes. Suppose you are waiting for your friend at the chemistry lab. She is walking from the dorm to
the lab. Fifteen minutes have already passed since the time she left the dorm. What is
the probability that she will arrive at the chemistry lab in the next 10 minutes?
(4) A manufacturer is concerned about the quality of a particular item produced in one of its
facilities. The facility operates with three 8-hour shifts of employees during the day. At the
end of each shift a random sample of the item is selected and each item checked against
the required specifications. The selected items are classified as being either Acceptable
or Unacceptable.
The following table summarizes the results.
Shift
Quality
One Two Three
Acceptable
96 118
64
Unacceptable 14
12
6
Fill in the blanks in the following statement.
Considering the entire day’s production of all sampled items the proportion produced by
Shift One that are Unacceptable is
, but among items produced by
Shift One the proportion of Unacceptable items is
.
(5) A marketing research firm wishes to determine if the adult men in Laramie, Wyoming
would be interested in a new upscale men’s clothing store. From a list of all residential
addresses in Laramie, the firm selects a simple random sample of 100 and mails a brief
questionnaire to each.
What is the population of interest?
(a) All adult men in Laramie, Wyoming.
(b) All residential addresses in Laramie, Wyoming.
(c) The members of the marketing firm that actually conducted the survey.
(d) The 100 addresses to which the survey was mailed.
What is the sample in this survey?
(a) All adult men in Laramie, Wyoming.
(b) All residential addresses in Laramie, Wyoming.
(c) The members of the marketing firm that actually conducted the survey.
(d) The 100 addresses to which the survey was mailed.
What do we know about the chance that all 100 homes in a particular neighbourhood in
Laramie end up being the sample sample of residential addresses that is selected?
(a) It is the same for any other set of 100 residential addresses.
(b) It is exactly 0. Simple random samples will spread out the addresses selected.
(c) It is reasonably large due to the “cluster” effect.
(d) It is 100 divided by the size of the population of Laramie.
(6) Let the random variable X be the number of repair calls that an appliance shop may
receive during an hour. The distribution of X is given below:
Value of X 0 1
2
3
4
Probability ? 0.3 0.12 0.18 0.2
Find the mean and standard deviation of X . What information does this provide to the
manager of the repair shop?
(7) At the end of a production run manufacturing rubber gaskets, items are sampled at random and inspected to determine if each item is Acceptable (A), or Defective (D). Suppose
it is planned to select two items and determine if each is either A or D.
(a) What is the sample space of outcomes?
A. S = {AA, AD, DD, DA}
B. S = {A, D}
C. S = {AA, DD}
D. Depends upon the probabilities assigned to each event.
E. Cannot be determined from the information given.
(b) Which set of outcomes describes the event that at least one of the items is defective?
A. {AA, AD, DD}
B. {AD, DA, DD}
C. {DD}
D. {AA, AD, DA}
E. {AA, DD}
(8) Ignoring twins and other multiple births, assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a
girl both equal to 0.5. What is the probability that at least one of the next two babies is a
boy?
(9) Suppose that the actual proportion of undergraduates at Johns Hopkins University who
feel that drinking is a problem among college students is 67%. A simple random sample
of 50 undergraduates at Johns Hopkins found that 60% of those sampled felt that drinking
was a problem among college students. Which value(s) can be labeled as parameter(s)?
(10) Should you have a cup of coffee to make you more alert when studying for a big test? A
study on the effect of caffeine involved asking volunteers to take a memory test 20 minutes
after drinking cola. Some volunteers were randomly assigned to drink caffeine-free cola,
some to drink regular cola (with caffeine), and other a mixture of the two (getting half a
dose of caffeine). For each volunteer, a test score (the number of items recalled correctly)
was recorded. The volunteers were not told which type of cola they had been given, but
the researchers for the study prepared the cups of cola right on the spot (out of sight of
the volunteers).
(a) What type of study is this?
(b) What is the response variable?
(c) What is the explanatory variable?
(d) Which of the basic principles of statistical design were used in this study?
(e) The study will be better if the researcher controls for
, which are
not part of the original study but may affect the outcomes being measured.
(f) Can you think of any lurking or confounding variables in this study that could affect
the results? Can you improve the study by controlling for these (if so, specify how)?
(11) Suppose there are three balls in a box. On one of the balls is the number 1, on another
the number 2, and on the third is the number 3. You select two balls at random and without replacement from the box and note the two numbers observed. The sample space
S consists of the three equally likely outcomes {(1, 2), (1, 3), (2, 3)} (disregarding order).
Let X be the sum of the two balls selected. Find the distribution of X .
(12) The American Veterinary Association claims that the annual cost of medical care for dogs
averages $100 with a standard deviation of $30. The cost for cats averages $120 with
a standard deviation of $35. Some basic algebraic and statistical steps show us that
the average of the difference in the cost of medical care for dogs and cats is then $100$120=-$20. The standard deviation of that same difference equals $46. If the difference
in costs follows a Normal distribution, what is the probability that the cost for someone’s
dog is higher than for the cat?
(a) 0.2839
(b) 0.3319
(c) 0.6618
(d) 0.7161
ANSWERS (not solutions...):
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
Only C is TRUE.
No.
0.9498.
0.045, 0.127.
A, D, A.
1.88, 1.437.
C, B.
0.25.
67%.
Experiment; Test score; Amount of caffeine; Control, randomization, repetition, blinding;
Confounding variables.
(11) The values 3, 4, 5 are equally likely.
(12) B.