1. Say you want to estimate the height of all the people in your town. You decide
to choose a sample of 1000 residents, find each height in the sample, and then
take the average.
A. Split the students into two groups based on gender. Assume 52% of the
population is female and 48% is male. How many males would there be in
the sample in your randomly chosen group? (3 points)
B. What type of sample is this? (3 points)



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.