QUESTION 1
a) The table below gives the frequency distribution of marks obtained by a group of students in a class test.
Marks
|
3
|
4
|
5
|
6
|
7
|
8
|
Frequency
|
5
|
x-1
|
x
|
9
|
4
|
1
|
i) Find the value of x if the mean for the distribution is 5.
ii) What is the modal mark.
iii) Find the mean absolute deviation.
iv) Find the sample variance and the sample standard deviation
b) By using the phrases
“correct decision”
or
“wrong decision”, complete the decision table for hypothesis testing below. Where the decision is wrong, state the type of error committed.
DECISION
|
H0
is false
|
H0
is true
|
Reject H0
|
|
|
Fail to Reject H0
|
|
|
(c) In the test of a certain hypothesis the
p-value
corresponding to the test statistics is
0.0316. Can the null hypothesis be rejected at the;
i) 01
level of significance?
ii) 05
level of significance?
Justify your answers.
QUESTION 2
The following data represents the amount in kg of fertilizer applied to equal size of plots and the yields in kg of maize.
PLOT
|
AMOUNT OF FERTILIZER(X)
|
YIELDS(Y)
|
A
|
2
|
7
|
B
|
1
|
3
|
C
|
3
|
8
|
D
|
4
|
10
|
i) Calculate and interpret the correlation coefficient for X and Y
ii) Calculate and interpret the least square regression of Y on X
c) Find the value of
a, b, …, f
in the one-way
ANOVA
table below.
Source
|
SS
|
df
|
MS
|
F
|
Treatment
|
361.5
|
b
|
60.25
|
f
|
Error
|
a
|
21
|
d
|
|
Total
|
821.7
|
c
|
e
|
|
QUESTION 3
Suppose that the random variable, X, is a number on the biased die and the p.d.f. of X is as shown below;
X
|
1
|
2
|
3
|
4
|
5
|
6
|
P(X=x)
|
1/6
|
1/6
|
1/5
|
k
|
1/5
|
1/6
|
Find;
- the value of
- E(X)
- E(X2)
- Var(X)
- P(1 X <>
b) If events
A
and
B
are such that they are independent, and
P(A) = 0.3
with
P(B) = 0.5;
i) Find
P(A n B)
and
P(AUB)
ii) Are
A
and
B
mutually exclusive?
iii) In how many ways can the letters of the word
STATISTICS
be arranged?
iv) State three (3) characteristic properties of a Normal Distribution curve.