Answer :
Sure, let's break down the solution to this question step by step.
### Part (a)
Question:
State the sampling technique Graham has used.
Answer:
The sampling technique Graham has used is stratified sampling. This method involves dividing the population into separate groups (strata) and then selecting a random or equal number of samples from each group. In this case, Graham has divided the population by gender and then selected an equal number of samples (50) from each group.
### Part (b)
Question:
Give two advantages and one disadvantage of this sampling technique.
Answer:
Advantages:
1. Ensures Adequate Representation of Each Subgroup: Stratified sampling ensures that each subgroup (in this case, males and females) is adequately represented in the sample. This leads to more accurate and reliable results because it accounts for the diversity within the population.
2. Reduces Potential Biases and Improves Accuracy: By ensuring each subgroup is proportionately represented, this method reduces the risk of bias that could result from over-representing or under-representing certain segments of the population, thereby improving the overall accuracy of the findings.
Disadvantage:
1. More Complex and Time-Consuming: Implementing stratified sampling can be more complex and time-consuming compared to simple random sampling because it requires dividing the population into strata and then sampling from each stratum separately.
### Part (c)
Question:
Explain how Graham could use a calculator or a random number generator to take a simple random sample from the males aged 25 to 35.
Answer:
To take a simple random sample from the list of 300 males:
1. Assign Numbers: Assign each male on the list a unique number from 1 to 300.
2. Generate Random Numbers: Use a calculator or a random number generator to generate 50 unique random numbers between 1 and 300.
3. Select Samples: Select the males corresponding to the randomly generated numbers. These individuals will be the ones from whom blood samples will be taken.
This method ensures that each male has an equal chance of being selected, hence maintaining the randomness of the sample.
### Part (d)
Question:
Explain how Graham could take a systematic sample of blood from females aged 25 to 35.
Answer:
To take a systematic sample from the list of 300 females:
1. Arrange List: First, arrange the 300 females in an alphabetical list.
2. Calculate Sampling Interval: Determine the sampling interval [tex]\( k \)[/tex]. The interval is found by dividing the total number of females by the desired sample size: [tex]\( k = \frac{300}{50} = 6 \)[/tex]. Hence, every 6th female will be sampled.
3. Select Starting Point: Randomly select a starting number [tex]\( r \)[/tex] between 1 and [tex]\( k \)[/tex]. For example, if [tex]\( r = 3 \)[/tex], the third female on the list is the starting sample.
4. Select Samples: Select every 6th female from the starting point. If the starting point is the 3rd female, the subsequent samples would be the 9th, 15th, 21st, and so on, until 50 samples are collected.
This method ensures that the samples are spread evenly across the entire population list, thus maintaining a systematic approach to sampling.
By following these steps, Graham can effectively implement both simple random sampling and systematic sampling techniques to obtain his required samples from the populations of interest.
### Part (a)
Question:
State the sampling technique Graham has used.
Answer:
The sampling technique Graham has used is stratified sampling. This method involves dividing the population into separate groups (strata) and then selecting a random or equal number of samples from each group. In this case, Graham has divided the population by gender and then selected an equal number of samples (50) from each group.
### Part (b)
Question:
Give two advantages and one disadvantage of this sampling technique.
Answer:
Advantages:
1. Ensures Adequate Representation of Each Subgroup: Stratified sampling ensures that each subgroup (in this case, males and females) is adequately represented in the sample. This leads to more accurate and reliable results because it accounts for the diversity within the population.
2. Reduces Potential Biases and Improves Accuracy: By ensuring each subgroup is proportionately represented, this method reduces the risk of bias that could result from over-representing or under-representing certain segments of the population, thereby improving the overall accuracy of the findings.
Disadvantage:
1. More Complex and Time-Consuming: Implementing stratified sampling can be more complex and time-consuming compared to simple random sampling because it requires dividing the population into strata and then sampling from each stratum separately.
### Part (c)
Question:
Explain how Graham could use a calculator or a random number generator to take a simple random sample from the males aged 25 to 35.
Answer:
To take a simple random sample from the list of 300 males:
1. Assign Numbers: Assign each male on the list a unique number from 1 to 300.
2. Generate Random Numbers: Use a calculator or a random number generator to generate 50 unique random numbers between 1 and 300.
3. Select Samples: Select the males corresponding to the randomly generated numbers. These individuals will be the ones from whom blood samples will be taken.
This method ensures that each male has an equal chance of being selected, hence maintaining the randomness of the sample.
### Part (d)
Question:
Explain how Graham could take a systematic sample of blood from females aged 25 to 35.
Answer:
To take a systematic sample from the list of 300 females:
1. Arrange List: First, arrange the 300 females in an alphabetical list.
2. Calculate Sampling Interval: Determine the sampling interval [tex]\( k \)[/tex]. The interval is found by dividing the total number of females by the desired sample size: [tex]\( k = \frac{300}{50} = 6 \)[/tex]. Hence, every 6th female will be sampled.
3. Select Starting Point: Randomly select a starting number [tex]\( r \)[/tex] between 1 and [tex]\( k \)[/tex]. For example, if [tex]\( r = 3 \)[/tex], the third female on the list is the starting sample.
4. Select Samples: Select every 6th female from the starting point. If the starting point is the 3rd female, the subsequent samples would be the 9th, 15th, 21st, and so on, until 50 samples are collected.
This method ensures that the samples are spread evenly across the entire population list, thus maintaining a systematic approach to sampling.
By following these steps, Graham can effectively implement both simple random sampling and systematic sampling techniques to obtain his required samples from the populations of interest.
