Answer :
Certainly! Let's go through the solutions to both parts of the question step by step.
### Part A: Calculating the Number of Males in the Sample
We need to determine the number of males in a sample of 1000 residents given that 48% of the population is male.
1. Determine the size of the sample: The sample size is 1000 residents.
2. Identify the percentage of males in the population: 48% of the population is male.
To find the number of males in the sample, we use the following formula:
[tex]\[ \text{Number of males} = \text{Total sample size} \times \left( \frac{\text{Percentage of males}}{100} \right) \][/tex]
Substituting the given values:
[tex]\[ \text{Number of males} = 1000 \times \left( \frac{48}{100} \right) \][/tex]
Calculate the result:
[tex]\[ \text{Number of males} = 1000 \times 0.48 \][/tex]
[tex]\[ \text{Number of males} = 480 \][/tex]
So, there would be 480 males in the sample.
### Part B: Type of Sample
In this sampling method, we are dividing the population into subgroups based on gender, and then we are selecting the sample from each subgroup proportionally.
This type of sampling, where the population is divided into distinct subgroups (strata) and samples are taken from each subgroup in proportion to its size, is known as stratified sampling.
So, the type of sample used here is a stratified sample.
### Part A: Calculating the Number of Males in the Sample
We need to determine the number of males in a sample of 1000 residents given that 48% of the population is male.
1. Determine the size of the sample: The sample size is 1000 residents.
2. Identify the percentage of males in the population: 48% of the population is male.
To find the number of males in the sample, we use the following formula:
[tex]\[ \text{Number of males} = \text{Total sample size} \times \left( \frac{\text{Percentage of males}}{100} \right) \][/tex]
Substituting the given values:
[tex]\[ \text{Number of males} = 1000 \times \left( \frac{48}{100} \right) \][/tex]
Calculate the result:
[tex]\[ \text{Number of males} = 1000 \times 0.48 \][/tex]
[tex]\[ \text{Number of males} = 480 \][/tex]
So, there would be 480 males in the sample.
### Part B: Type of Sample
In this sampling method, we are dividing the population into subgroups based on gender, and then we are selecting the sample from each subgroup proportionally.
This type of sampling, where the population is divided into distinct subgroups (strata) and samples are taken from each subgroup in proportion to its size, is known as stratified sampling.
So, the type of sample used here is a stratified sample.
