Assignment 1

STAT 2509 A
Assignment #1
(Review of STAT 2507)
DUE: May 22 nd , 2013 (to be handed in to your TA during the lab)
1. a) The set of all objects or measurements of interest to the sample collector is
(i) a statistic (ii) a population (iii) a sample (iv) a parameter
b) A numerical measure for a sample is referred to as
(i) a population (ii) a parameter (iii) a statistic (iv) a sample
2. Which of the following are measures of Central tendency?
a) mean & standard deviation b) mean & median c) mean & range
3. Identify the following variables as : “purely categorical” (or qualitative),
“categorical and ranked”, “quantitative and discrete” or “quantitative and
continuous”.
a) amount of time it takes to assemble a simple puzzle
b) province in which a person lives
c) number of students in a first grade classroom
d) rating of a newly elected politician (excellent, good, fair, poor)
e) final (i.e. letter) grade obtained in a statistics course
f) number of red cars in a parking lot
g) mark out of 100 obtained on a school entrance test
4. Classify each of the following quantities as either a parameter or a statistic:
(i) x (ii)
2
σ (iii) µ (iv)
2
s (v) 1
5. Find the following values from the tables:
1
β (vi) β 1
a) z 0.
025 b) z 0.
975 c) z 0.
03 d) t 9;
0.
05 e) − t9;
0.
05 f) t
9;
0.
95
ˆ

6. Consider a normal population distribution with the value of σ known.
a) What is the confidence level for the interval
(i) x ± 1.
96σ
n (ii) x ± 2.
24σ
n (iii) x ± 3.
09σ
n
b) What value of z in the confidence interval formula
( x − zα
2 σ n,
x + zα
2 σ n )
results in a confidence level of
(i) 89.68% (ii) 99.20% (iii) 75.40%
7. For any hypothesis test:
a) Explain what the null and alternative hypotheses are.
b) What are the two types of error that may be made?
8. Given that the population variance is defined by
2
σ
=
1
N
∑ N i=
1
2
( x − µ )
where: N is the population total (i.e. total number of the observations in the
population) and µ the population mean.
Show that
⎛
N
2 ⎞
⎜ ⎛ ⎞
⎜ ⎟
⎜ ∑ x ⎟
N
i
⎠ ⎟
2 1 2
=
⎝ i=
1
σ ⎜∑
xi
− ⎟ .
N ⎜ i=
1 N ⎟
⎜
⎟
⎝
⎠
i
2