STAT 2509 C Assignment #1 (2016)

| August 31, 2017

Question
1
STAT 2509 C
Assignment #1
(Review of STAT 2507)
DUE DATE: Wednesday, January 20th, 2016 (to be submitted in class)
Answer all of the following questions.
1. The process of using information from a sample to draw conclusions about the entire
population is called
(a) sampling (b) the scientific method
(c) statistical inference (d) descriptive statistics
2. A numerical measure computed to describe a characteristic of a sample is called a
(a) parameter (b) statistic (c) sample (d) population
3. Identify the following variables as : purely categorical (or qualitative), categorical and
ranked, quantitative and discrete or quantitative and continuous.
a) the number of students who get a final grade greater than 80%
b) dress size: 3, 5, 7, 9, 11, 13, 15, 17
c) weight of a newborn in kg
d) rating of a politician as: excellent, good, fair, poor
e) mark out of 100 obtained on a statistics test
f) letter grade obtained on a statistics test
g) number of milk bags bought by a family weekly
4. Classify each of the following quantities as either a parameter or a statistic:
(i) x (ii) 2
? (iii) µ (iv) 2
s (v) ? 0
(vi) 1
ˆ?
5. Find the following values from the tables:
a) .0 3015 z b) .0 6985 z c) .0 002 z d) 11 .0; 05 t e) 11 .0; 05 ? t f) 11 .0; 95 t
6. Consider a normal population distribution with the value of ? known.
a) What is the confidence level for the interval
(i) x ± .1 96? n (ii) x ± .2 58? n (iii) x ± .3 09? n
2
b) What value of z in the confidence interval formula
(x z ? n x z ? n ) ? 2 ? 2 ? , +
results in a confidence level of
(i) 89.68% (ii) 99.20% (iii) 75.40%
c) Would a 90% C.I. be narrower or wider than the 99.20% C.I. in b)?
7. a) Define 2-sided and 1-sided hypotheses and give the steps involved in their
testing.
b) For any hypothesis test, what are the two types of error that may be made?
8. If k is a constant and X and Y are random variables, then
a) (i) E(k)=?, (ii) E(kX)=?, (iii) E(X±Y)=?
b) (i) V(k)=?, (ii) V(kX)=?, (iii) V(X±Y)=? Also show what happens when X and
Y are independent of each other?
9. ANOVA method for a linear regression gives following:
TSS = ?( )
=
?
n
i
i
y y
1
2
,
where TSS is the total variation in the data. Show that
TSS = ?( )
=
?
n
i
i
y y
1
2
=
n
y
y
n
i
i n
i
i
2
1
1
2
?
?
?
?
?
?
?
?
?
=
=
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STAT 2509 C Assignment #1 (2016) Solution
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