Home » VCE » Maths Methods U3 & 4 Master Notes » Sample Proportion Distribution

# Sample Proportion Distribution

## 4.3 Approximating Sample Proportion Distribution

#### Approximating Sample Proportion Distribution

• Previously in 4.2 Distribution of Sample Proportion, we have seen that we can assume the distribution of a sample proportion. With that said, since each random sample we use will be different for each experiment, it is almost certain that the sample proportion will be different each time.
• For instance, suppose there are 55% male, 45% female in Australia. However, we do not know this, and we want to test for the proportion of males to females in Australia. A random sample of 100 people is chosen and apparently 58 of them is male, hence \hat{p}=0.58. Repeat the process again, this time we have 44 males, therefore \hat{p}=0.44. Repeat the experiment 200 times, and we would have something like this:
Read More »4.3 Approximating Sample Proportion Distribution

## 4.2 Distribution of Sample Proportion

#### Sampling Distribution of a Small Proportion

• Recall that

\text { Sample proportion, }\ \hat{p}=\frac{\text { number in population with attribute }}{\text { population size }}

and can be treated as a random variable.

• In a small enough population, we are able to list out all the possible samples, the probability of getting each sample, and therefore the sample proportion.
• Therefore, we are able to construct the probability distribution of \hat{p}.
• The distribution of a statistic which is calculated from a sample (such as the sample proportion) is called a sampling distribution.
Read More »4.2 Distribution of Sample Proportion

## Sampling and Estimation

This tutorial covers material encountered in chapter 17 of the VCE Mathematical Methods Textbook, namely: Sampling and estimation methods The population, sample and their proportions… Read More »Sampling and Estimation