STATISTICS 111
HOMEWORK 8 (due 10/30/2015)
1.
Let 1 be the probability that a woman is left-handed and 2 be the probability that a man
is left-handed. We are interested in the question of whether men and women differ in their
tendency to be left-handed. T
STATISTICS 111
HOMEWORK 9 (due 11/6/2015)
Informal introduction to hypothesis testing
We have started hypothesis testing in class. Questions 1 and 2 in this homework give an informal
introduction to problems of hypothesis testing in the simple context of
STATISTICS 111
HOMEWORK 3 due 9/18/2015
This homework mainly concerns various event probability calculations, followed
by a practical application of probabilities of events.
1. Suppose that a fair die is to be rolled twice. Use appropriate formulas given
STAT 111 - Fall 2015
HOMEWORK 2 (Due Friday 11 September at recitation class.)
Remember the following two notes from Homework 1:
NOTE 1: Homeworks will be handed out in Friday recitation classes and your answers should
be handed in during Friday recitatio
STATISTICS 111
HOMEWORK 10 - due 11/13/2015
1. (i) We are currently using a drug for a certain medical complaint which is known to cure a
patient with probability 0.8. A new drug is claimed to have a higher cure rate than the currently
used drug. To test
STATISTICS 111
HOMEWORK 6 due 10/16/2015
NOTE: Because of the mid-term break there will not be a recitation class on
October 9. Thus this homework will be due in at recitation class on October
16. Because of this, this homework is longer than usual and ca
STATISTICS 111
HOMEWORK 5 due 10/2/2015.
The theme of these questions will be continued later, so keep a copy of your answers.
1. Suppose that a fair die is to be rolled twice. In Homework 3, Question 1, you found
the probabilities that the sum of the two
STAT 111 - Fall 2015
HOMEWORK 1 (Due Friday 4 September at recitation class.)
NOTE 1: Apart from this homework, homeworks will be handed out in Friday recitation
classes and your answers should be handed in during Friday recitation classes one week later.
STATISTICS 111
HOMEWORK 4 due in at class 9/24/2015
1. The random variable X has a binomial distribution with index n = 14 and parameter
= 0.4. Use your binomial chart to find (i) the probability that X = 6, (ii) the probability
that X is either 5, 6 or
or the conservative
p
1/n
p
Estimation of a mean
to
p+
p
1/n.
Once the relevant experiment has been carried out you will have data x1 , x2 , ., xn . You
regard these data values as the observed values of n iid random variables X1 , X2 , ., Xn , each
havi
Probability theory (deduction, implication) !
Calculates probabilities
associated with possible
data
Starts with some assumption about reality
Statistics (induction, inference)
Makes some
about reality
inference
Starts with data
The coin example above ill
(c) Prob(3.56 X 4.24).
[2+2+2=6 points]
7. Suppose that we know that the height of a woman chosen at random is a random variable
having a normal distribution with mean 67 inches, variance 16 (inches squared). Find:(a) the probability that the height of a
STAT 111 - Fall 2015
HOMEWORK 1 (Due Friday 4 September at recitation class.)
NOTE 1: Apart from this homework, homeworks will be handed out in Friday recitation
classes and your answers should be handed in during Friday recitation classes one week later.
STAT 111 - Fall 2015
HOMEWORK 2 (Due Friday 11 September at recitation class.)
Remember the following two notes from Homework 1:
NOTE 1: Homeworks will be handed out in Friday recitation classes and your answers should
be handed in during Friday recitatio
5. (a) The random variable X comes from a normal distribution with mean 1 1, variance 16. Find
(i) Prob (X > 14),
(ii) Prob (X < 9),
(iii) the number A such that Prob (X < A) = 0.7734. [12]
(b) Suppose now that X1, X2, X3 and X4 are all independent random
STATISTICS 111
HOMEWORK 5 due 10/2/2015.
The theme of these questions will be continued later, so keep a copy of your answers.
1. Suppose that a fair die is to be rolled twice. In Homework 3, Question 1, you found
the probabilities that the sum of the two
STATISTICS 111
HOMEWORK 4 due in at class 9/24/2015
1. The random variable X has a binomial distribution with index n = 14 and parameter
= 0.4. Use your binomial chart to find (i) the probability that X = 6, (ii) the probability
that X is either 5, 6 or
alternative hypothesis which tells us whether it is one-sided up or one-sided down.
Suppose that the alternative hypothesis is that a woman is more likely to be pro-choice than
a man is. If this alternative hypothesis is true, we would expect that or111 (
Notes on z and c2 in 2 2 tables.
1. z.
Suppose that we have the following data:
women
men
total
pro-choice
o11
o21
c1 (= x11 + x21 )
pro-life
o12
o22
c2 (= x12 + x22 )
total
r1 (= x11 + x12 )
r2 (= x21 + x22 )
n
In this table r1 and r2 are row totals, c1
answer is, it must depend on the above probability theory calculation.)
[4 points]
Events
3. A die is to be rolled once. The event A is: An even number turns up and the event B
is: a 4, a 5 or a 6 turns up. Describe in words what the events A [ B and A \
STATISTICS 111
HOMEWORK 6 due 10/16/2015
NOTE: Because of the mid-term break there will not be a recitation class on
October 9. Thus this homework will be due in at recitation class on October
16. Because of this, this homework is longer than usual and ca
STATISTICS 111 - MID-TERM EXAM 2015
Notes (i) Points for each question, or part of question, are indicated in brackets [.]
(ii) Read each question carefully. More marks are usually lost by not doing this than
by giving incorrect answers.
(iii) Unless told
used in medical contexts, is defined as
RR =
Prob(B|A)
.
Prob(B|Ac )
State in words what this relative risk means, and calculate its numerical value from the
probabilities given above.
[3 + 3 = 6 points]
TOTAL: 50 points.
2
(c). Present all your probabilities in fractional form (i.e. in the form a/b, where a and b
are integers (i.e. whole numbers), not in decimal form such as 0.wxyz. Also, use the same
value of the denominator b for all the probabilities and other quantities
5(ii). The short formula for the variance of a binomial random variable with index n and
parameter is n(1 ). Use this formula to compute the variance of a random variable
having a binomial distribution with index 11 and parameter 0.4. Check that your calc
ders in which we can get three heads from five flips of a coin.
2. Use the formula
a coin.
n
x
[8 points]
to find the number of ways of getting three heads from six flips of
[5 points]
3. The original derivation of the word choose is that nx is the number
STATISTICS 111
HOMEWORK 3 due 9/18/2015
This homework mainly concerns various event probability calculations, followed
by a practical application of probabilities of events.
1. Suppose that a fair die is to be rolled twice. Use appropriate formulas given
One Sample t-Test in VIP
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