A large company surveyed its staff to investigate the awareness of company policy.
The company employs 6000 full time staff and 4000 part time staff.
Describe how a stratified sample of 200 staff could be taken.
- Label full-time staff 1 - 6000, part-time 1 - 4000
- Use a random number generator to select
- Simple random sample of 120 full-time staff and 80 part-time staff
- ( 6000 / 10 000 x 200 = 120 )
- ( 4000 / 10 000 x 200 = 80 )
Explain an advantage of using a stratified sample rather than a simple random sample.
- Reflects population structure
A telephone directory contains 50 000 names.
A researcher wishes to select a systematic sample of 100 names from the directory.
Explain in detail how the researcher should obtain such a sample.
- Randomly select a number between 00 and 499
- ( 50 000 / 100 = 500 )
- ( Either 1 - 500 or 0 - 499 )
- Select every 500th person
Give one advantage and one disadvantage of quota sampling.
( A telephone directory contains 50 000 names.
A researcher wishes to select a systematic sample of 100 names from the directory. )
- It’s cheap
- It’s not a random process
Give one advantage and one disadvantage of systematic sampling.
- Suitable for large samples
- Requires a list of the population
- ( sampling frame )
A researcher is hired by a cleaning company to survey the opinions of employees on a proposed pension scheme.
The company employees 55 managers and 495 cleaners.
To collect data the researcher decides to give a questionnaire to the first 50 cleaners to leave at the end of the day.
Give 2 reasons why this method is likely to produce biased results.
- Only cleaners are used in the sample
- Not a random sample
Explain briefly how the researcher could select a sample of 50 employees using a systematic sample.
( A researcher is hired by a cleaning company to survey the opinions of employees on a proposed pension scheme.
The company employs 55 managers and 495 cleaners. )
- Label employees ( 1 - 550 )
- Select from the first 11 using random numbers
- Then select every 11th person from the list
- ( 550 / 50 = 11 )
Explain briefly how the researcher could select a sample of 50 employees using a stratified sample.
( A researcher is hired by a cleaning company to survey the opinions of employees on a proposed pension scheme.
The company employs 55 managers and 495 cleaners. )
- Label managers ( 1 - 55 ) and cleaners ( 1 - 495 )
- Use random number generator to select 5 managers and 45 cleaners
- ( 55 / 550 x 50 = 5 )
- ( 495 / 550 x 50 = 45 )
Describe one advantage and one disadvantage of quota sampling.
( Out of context )
- Doesn’t require a sampling frame
- Non responses are not recorded
Describe one advantage and one disadvantage of simple random sampling.
- Free from bias
- Not suitable for large sample size
State two reasons why stratified sampling might be chosen as a method of sampling when carrying out a statistical survey.
- Population divides into distinct strata
There are 64 girls and 56 boys in a school.
Explain briefly how you could take a random sample of 15 pupils using a simple random sample.
- Allocate a number between 1 and 120 to each pupil
- Use a random number generator to select 15 different numbers between 1 and 120
- Pupils corresponding to this number become the sample
There are 64 girls and 56 boys in a school.
Explain briefly how you could take a random sample of 15 pupils using a stratified sample.
- Allocate numbers 1 to 64 for girls and 1 to 56 for boys
- Select 8 random numbers between 1 to 64 for girls
- ( 64 / 120 x 15 = 8 )
- Select 7 random numbers between 1 to 56 for boys
- ( 56 / 120 x 15 = 7 )
Explain how to obtain a sample from a population using stratified sampling.
Give one advantage and one disadvantage of each sampling
method.
- Take a random sample from mutually exclusive groups of the population
- Sample sizes within the strata are proportional to numbers
in each strata in the population - Advantage = Individual estimates for strata available
- Disadvantage = Difficult if strata are large
Explain how to obtain a sample from a population using quota sampling.
Give one advantage and one disadvantage of each sampling
method.
- Non-random sampling from groups of the population
- Advantage = Cheap
- Disadvantage = Non-responses are not recorded
Explain what you understand by a sampling unit.
- Individual member or element of the population or sampling frame
Explain what you understand by a sampling frame.
- A list of all sampling units
Before introducing a new rule, the secretary of a golf club decided to find out how members might react to this rule.
Explain why the secretary decided to take a random sample of club members rather than ask all the members.
- Cheaper
Suggest a suitable sampling frame.
( Before introducing a new rule, the secretary of a golf club decided to find out how members might react to this rule. )
- List of all club members
Identify the sampling units.
( Before introducing a new rule, the secretary of a golf club decided to find out how members might react to this rule. )
- Club members
Explain what you understand by a census.
- A census is when every member of the population is investigated
Each cooker produced at GT Engineering is stamped with a unique serial number. GT Engineering produces cookers in batches of 2000.
Before selling them, they test a random sample of 5 to see what
electric current overload they will take before breaking down.
Give one reason, other than to save time and cost, why a sample is taken rather than a census.
- There would be no cookers left to sell
Suggest a suitable sampling frame from which to obtain this sample.
( Each cooker produced at GT Engineering is stamped with a unique serial number. GT Engineering produces cookers in batches of 2000.
Before selling them, they test a random sample of 5 to see what
electric current overload they will take before breaking down. )
- A list of the unique identification numbers of the cookers
Identify the sampling units.
( Each cooker produced at GT Engineering is stamped with a unique serial number. GT Engineering produces cookers in batches of 2000.
Before selling them, they test a random sample of 5 to see what
electric current overload they will take before breaking down. )
- A cooker
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Proof by contradiction ( Algebratic Methods )12
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Trigonometric Equations and Identities7
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Modelling with differentiation2
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Pulleys18
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Binomial expansion12
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Proof By Exhaustion10
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Simplifying Rational Expressions6
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Sketching Graphs2
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The Discriminant3
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The Factor Theorem3
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Partial Fractions5
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Representations Of Data32
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Sampling Methods24
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Hypothesis Testing18
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Statistical Distribution12
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Sequences And Series33
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Moments14
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Functions And Graphs4
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Trigonometry7
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Radians2
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Forces And Friction4
