In a certain town, there are 30,000 registered voters, of...

In a certain town, there are $30,000$ registered voters, of whom $12,000$ are Democrats. A survey organization is about to take a simple random sample of $1,000$ registered voters. There is about a $50-50$ chance that the percentage of Democrats in the sample will be bigger than $\longrightarrow$ Fill in the blank, and explain.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Sampling Distribution of the Sample Proportion

This concept refers to the probability distribution of the sample proportion calculated from all possible simple random samples of a fixed size. It is centered at the true population proportion, meaning that there is an equal chance to obtain a sample proportion either above or below the population proportion.

Central Limit Theorem

In the context of sample proportions, the Central Limit Theorem states that when the sample size is sufficiently large, the sampling distribution of the sample proportion will be approximately normally distributed. This property allows statisticians to make probabilistic statements and confidence estimates regarding how the sample proportion relates to the true population proportion.

Simple Random Sampling

This sampling method ensures that every member of the population has an equal chance of being selected. It helps in obtaining a sample that is representative of the population, thereby reducing potential biases in estimates like the sample proportion.

Population Proportion

This is the ratio of individuals in a particular group to the total population. It serves as the fundamental benchmark in surveys and studies, informing what percentage of the entire group is expected to have a certain attribute.

Transcript

Please give Ace some feedback