STA 1011: Introduction to Statistics
Assignment 4 Academic year 12/13, Second term
Due Time: 19:00pm, March 11th ,2013. All data sets are in Elearning/Course Content/Data Set
1. A statistical analysis of 1000 long-distance telephone calls made from the he
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STAT1011: Introduction to Statistics
Assignment 5
Academic year 12/13, First term
1. A population has four members (called A, B, C, and D). You would like to select a random sample
of n = 2, which you decide to do in the following way: Flip a coin; if it
8. What is your decision?
9. What is your conclusion?
_ Exerise 81 "
For Exercises 1 through 25, perform each of the following
Steps.
a. State the hypotheses and identify the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the dec
Examples on Probability (STAT1011, 13-14)
1. A basketball team consists of 6 black and 4 white players. If the players are
randomly divided into two groups of size 5 each, what is the probability that
both groups will have the same number of black players
Summary of Chapter 6
1
Concepts
Condence Interval Estimate for :
1. is known:
Two-sided: A 100(1 )% condence interval (C.I.) on is given by
Concepts
Examples
X Z/2 X + Z/2
n
n
One-sided: A 100(1 )% upper (or lower)-condence bound for is
X + Z
n
or
X Z
Computation of V ar(X) :
Assume that X is a random variable with probability distribution
x1
X
p(x) p(x1 )
xN
p(xN )
N
V ar(X) = 2 =
[xi E(X)]2 p(xi )
i=1
N
[x2 2xi E(X) + (E(X)2 ]p(xi )
i
=
i=1
N
N
N
x2 p(xi )
i
=
2
2E(X)
i=1
p(xi )
xi p(xi ) + (E(X)
i
STAT1011: Introduction to Statistics
Assignment 6
Academic year 12/13, First term
1. The manager of a paint supply store wants to estimate the actual amount of paint contained in
1-gallon cans purchased from a nationally known manufacturer. The manufactur
STAT1011 (14-15, 2nd term) Final solution
1. (a) Since X1 , . . . , X10 N (2, 25) independently, T =
Z = T20
, and we have Z N (0, 1). So
250
22 20
P (T > 22) = P Z >
250
(b) Since
(n1)S 2
2
2 (n 1), let U =
9S 2
,
25
X
.
/ n
i=1
Xi N (20, 250). Let
!
STAT1011 (15-16, 2nd term) Quiz1 (Total = 15 marks)
Part A [12 marks]
[Show your steps clearly and use at least 3 significant figures for numbers in
intermediate steps and the final answer]
1. A box contains a white balls, b red balls and c blue balls. Al
STAT1011 Assignment 1 (Due Date: Monday, Feb 6, 2017 [6:00pm])
1. Suppose that a professor knows that the test score of a student taking his final
examination is a random variable with mean 75 and variance 25.
a) Give an upper bound to the probability tha
9.13
a. H0 : = 12.1
H1 : 12.1
b. Type I Error: When it is true, reject H0 which the mean hours studied is 12.1 hours.
c. Type II Error: When it is false, fail to reject H0 which the mean hours studied is
12.1 hours.
9.48
a. Test Statistic = -28.28427125 <
DSME 5110BA
Statistical Analysis
Assignment 2
This assignment is due by 11:59 pm on 27th October (Thursday). Each group shall
submit a copy to Dr. Yuen: andrewyuen@baf.cuhk.edu.hk and Cindy:
cindylau@baf.cuhk.edu.hk. In your assignment front page, please
STAT1011: Introduction to Statistics
Assignment 3
Academic year 12/13, First term
1. Suppose that there are two alternative investments for the coming year. The rst investment is
a mutual fund that consists of the stocks that comprise the Dow Jones Indust
STAT1011: Introduction to Statistics
Assignment 1
Academic year 12/13, First term
Note: Please download all data sets on e-learning/STAT1011/Course Content/Data Sets.
1. For each of the following variables, determine whether the variable is categorical or
Find quartiles Q1, Q2, Q3 and mode:
x1 , , xn raw data
n sample size
qi the rank (position) of Qi
[qi ] the integer part of qi , i = 1, 2, 3. e.g. [3.3]=3, [4.8]=[4]
Find Q2 (the second quartile or median):
Step 1: Take an ordered array: x(1) x(2) x(n) .
)
Whisker extends to
smallest data point within
1.5 interquartile ranges from
first quartUe
First quartile
o
1.5 JQR
Second quartile
Third quartile
o
0
" I
Outliers
I.
Whisker extends to
largest data point within
1.5 interquartile ranges
from third Quarti
STAT 1011, Assignment 6
Suggested solution
1.
a.
!.!"
!
!
!.!"
= 0.995 2.58
!"
= 0.995 0.0073
The 99% confidence interval is (0.9877, 1.0023). You conclude with 99% confidence that the
population mean amount of paint included in a 1-gallon can is between
STAT 1011, Assignment 1 Solution. 2012-2013, term 1
1.a. Numerical and continuous
b .Categorical
c. Categorical
d. Numerical and Discrete
2.a. Reason to choose former one: obtain more accurate data than the latter one; available to do
further detailed ana
STAT 1011 Assignment7
Suggested Solution
1.
a.
, where
Under
b.
and
the population mean amount of paint
. The
test statistics is between two critical values. Hence, at the 0.05 level of
significance, there is no enough evidence that the population mean am
STAT1011: Introduction to Statistics
Solution of Assignment 5
Academic Year 12/13, First Term
1.
The sampling method described in the question is not a simple random sample because not all
samples of
have an equal chance of being selected. For example, th
STAT1011 Assignment2
Suggested Solution
1.
a. We can use mean(), median(), quantile() function in R to compute the mean, median, first
quartile, and third quartile.
> data<-c(26,28,20,20,21,22,25,25,18,25,15,20,18,20,25,25,22,30,30,30,15,20,29)
> mean(dat
STAT1011: Introduction to Statistics
Solution for Assignment 3
Academic Year 12/13, First Term
1. Let X be the assets invested in the Dow Jones Fund, Y be the assets
invested in a weak-economy fund and P be the portfolio assets.
Then P = X + (1 )Y , where
STAT1011: Introduction to Statistics
Assignment 4
Academic year 12/13, First term
Note: Please download all data sets on e-learning/STAT1011/Course Content/Data Sets.
1. Suppose the cumulative distribution function of the random variable X is
0
x < 2
0.25
STAT1011: Introduction to Statistics
Assignment 2
Academic year 12/13, First term
Note: Please download all data sets on e-learning/STAT1011/Course Content/Data Sets.
1. The data in the le bankcost1.xls contain the bounced check fees, in dollars, for a sa
STAT1011: Introduction to Statistics
Assignment 7
Academic year 12/13, First term
1. The manager of a paint supply store wants to determine whether the mean amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer is actua
Assignment 1
Practice questions solution
2.16
2.18
(a)
Electricity Costs
$80 to $99
$100 to $119
$120 to $139
$140 to $159
$160 to $179
$180 to $199
$200 to $219
(c)
The majority of utility charges are clustered between $120 and $180.
Percentage
8%
14
18
1.
6.51
a. 0.5
b. 0.308538
c. 0.158655
d. 0.02275
e(a). 0.476078
e(b). 0.347037
e(c). 0.272036
e(d). 0.10145
f. With a large standard deviation, there is a higher possibility that the company will
suffer a lost. On the other hand, there is a lower possibi
Tutorial 2
1.
Suppose we want to select 6 numbers from 1,2, ,44. How many possible
choices do we have if:
a.
b.
c.
d.
the ordering matters, and no same numbers are allowed;
the ordering matters, and same numbers are allowed;
ordering doesn't matter, and n
A
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STAT1011 Example 2
1. In a distribution of 160 values with a mean of 72, by using the Chebyshevs
theorem, we conclude that at least 120 values fall within the interval [67, 77]. Use
the Chebyshevs theorem again, at least what proportion of values fall in