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? 10 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
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?
- 10 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
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
|
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 <5)
b) If
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
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