PART ONE – Please Tick √ Only One Answer (18 marks)
Q1: _____ occurs when every member of a population has an equal chance
of being selected for a sample
A: Systematic sampling
B: Stratified random sampling
C: Simple random sampling
D: Area probability sampling
Q2: Systematic sampling can produce a very biased sample when:
A: There is no available sampling frame.
B: The population is too large
C: There is a structure to the sampling frame.
D: The population is too heterogeneous
Q3: You are interested in factors that predict loyalty to sports teams. Which
of the following would be an example of a purposive sampling strategy?
A: Attend the next game of a winning professional sports team
B: Obtain a directory of season ticket holders of a professional sports team
C: Put a notice in the local newspapers announcing the study
D: Ask friends for referrals of sports fanatics to your study
Q4: Convenience samples are frequently used in student research because
they:
A: Are more appropriate for statistical analysis
B: Yield representative samples
C: Are preferred by instructors
D: Take less time and money
Q5: Which of these is a probability sampling technique?
A: Snowball sampling
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B: Convenience sampling
C: Systematic random sampling
D: Quota sampling
Q6: Which of these is a non-probability sampling technique?
A: Purposive
B: Multi-stage
C: Random
D: Cluster
Q7: The mean is:
A: A summary of the data in terms of the most common value of the data
B: A summary of the data that is always half way between the maximum and
minimum value of the data
C: A summary of the data estimated by adding all the numbers, and dividing by
the number of the data minus one
D: None of the above
Q8: The variance is always:
A: The square of the standard deviation
B: A measure that changes if you add a constant to all of the data
C: A measure of how the data is distributed around the median
D: None of the above
Q9: The null hypothesis is regarded as:
A: The simplest explanation for the data collected
B: The original statement which is simple and specific
C: Proved to be incorrect by a significant result
D: None of the above
Q10: If we want an average distance to the mean, why can't we just add up
all the differences to the mean and take the average?
A: It is too time consuming
B: The data are not normally distributed
C: The data will be skewed
D: The negative and positive values will cancel each other out
Q11: Why do you need standard deviation?
A: To calculate the median
B: To calculate the mean
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C: To understand the lowest and highest points in the data
D: To describe how far the data are spread around the mean
Q12: A standard deviation of 0 means?
A: You cannot have a 0 standard deviation
B: There is an extreme amount of variability
C: The variance is – 1
D: All values in the sample are the same
PART TWO
1) True or False (4 marks)
The mean of a sample always divides the data into two equal halves – half
larger and half smaller in value than itself
The sum of the squares of the deviations from the mean will sometimes be
negative
A set of test paper was machine scored, later it was discovered that two
points should be added to each score
The mean score should also be increased by two points
The standard deviation should also be increased by two points
2) Please identify each of the following as examples of (i) discrete (D) or (ii)
continuous variables (C): (6 marks)
The number of stop signs in towns of less than 500 people
The length of time you undertake an interview
The distance you can kick a football
The number of questions answered correctly on a standardised test
A poll of registered voters as to which candidate they support
The length of time required to answer a telephone
3) Please find the variance and standard deviation of (4 marks)
9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, and 4
4) If a sample has been taken from above, please fine the variance and
standard deviation of (4 marks)
9, 2, 5, 4, 12, and 7
PART THREE
1) A warehouse classifies its stock into three categories A, B, C. On all
category A items it promises a service level of 97% - so there is a
probability of 0.97 that the warehouse can meet demand immediately
from stock. On category B and C items it promises service levels of 94%
and 90%, respectively. If service levels are independent, what are the
probabilities that the warehouse can immediately supply an order for:
(9 marks)
a) One item of category A and one item of category B
b) One item from each category
c) Two items of category A and one B and three from category C
2) One evening a market researcher has to visit 12 houses, previous calls
suggest there will be someone at home in 85% of houses (12 marks)
a) Describe the probability distribution of the number of houses with people at
home
b) What is the probability that the researcher will find someone at home in
exactly 9 houses?
c) What is the probability there will be someone at home in exactly 7 houses?
d) What is the probability there will be someone at home in at least 10 houses?
PART FOUR
1) A mail order company charges a flat rate for delivery based on a mean
weight for packages of 1.75kg with a standard deviation of 0.5kg. Postal
charges now seem high, and a random sample of 100 packages has a
mean weight of 1.86kg. What does this show? Explain your answer
(12 marks)
2) Five factories report the following numbers of accidents in a five-year
period. Do these figures in Table 1 suggest that some factories have
more accidents than others? Explain your answer (15 marks)
3) A factory is doing some statistical analyses on the mean weight of a
product, but these analyses are only valid if the weights are normally
distributed. The product has a mean weight of 45g and standard
deviation of 15g. A sample of 500 units was taken, with weight
distribution given in Table 2. Does this suggest that the weights are
normally distributed? Explain your answer (16 marks)
Weight (grammes) Number of observations
Less than 10 9
10 – 19.99 31
20 – 29.99 65
30 – 39.99 97
40 – 49.99 115
50 – 59.99 94
60 – 69.99 49
70 – 79.99 24
80 – 89.99 16