Question

Question 1
Given an example on any one of the following sampling techniques (one example on only one technique).

 Simple random sampling

 Stratified random sampling

 Cluster sampling
Question 2
What is the difference between sampling error and non-sampling error? Give an example on each part.

Question 3

	B1	B2
A1	0.12	0.31
A2	0.08	0.49

a. Find P(A1)

b. Find P(A1 and B2)

c. Find P(A1|B2)

d. Find P(A2 or B1)

e. Find (B1 and B2)

Question 4
X the number of TVs a family owns in Doha. The table below shows the probability distribution.

X	P(X)
0	0.05
1	0.15
2	0.30
3	0.40
4	0.10

a. What is the probability that a family owns 3 TVs or less?

b. What is the probability that a family own exactly 2 TVs?

c. Find the standard deviation of the discrete random variable X

Question 5
A sales man finds that on average 0.15 of the TVs he sells are rejected each month because they are either too big or too small in size. The sales man has 20 TVs to sell each month.
a. What is the probability that at least 3 TVs be rejected.

b. What is the probability that 4 TVs are rejected.

Answer 1

(1) Simple random sampling -> 10 employees being chosen out of a hat from a company of 100 employees.
Stratified random sampling -> choosing 10 male students and 10 female students out of all male students and all female students of the class respectively.
Cluster sampling -> divide a class of students into 10 houses based on colour and then randomly select 2 houses from these 10 houses.

(2) Sampling error occurs when there is an inherent error in the sample that has been taken from the population. For example, we want to estimate the proportion of Democratic/Republican voters in the state, but we sample people from a particular city of that state.
Non-sampling error occurs during data collection and it stems from factors other than the sample selection. For example, refusal of people to participate in a survey to determine the average wage of citizens in a state.

(3) a. Find P(A1) = 0.12 + 0.31 = 0.43.
b. Find P(A1 and B2) = 0.31.
c. Find P(A1|B2) = 0.31/(0.31+0.49) = 0.3875.
d. Find P(A2 or B1) = 0.57 + 0.2 - 0.08 = 0.69.
e. Find (B1 and B2) = 0.

(4) a. Prob. = 0.05+0.15+0.3+0.4 = 0.9.
b. Prob. = 0.3.
c. E(X) = sum(X * P(X)) = 2.35. E(X²) = sum(X * X * P(X)) = 6.55.
Standard deviation = square root of (6.55 - (2.35²)) = 1.0137.