# STAT 2509 C Assignment #1 (2016)

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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