Statistics and Probability Lesson 1 Review: Random Variables and Probability Distributions

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What is the main difference between Random Sampling and Non-Random Sampling?

Random Sampling: Every unit of the population has the same probability of being included in the sample. Non-Random Sampling: Every unit of the population does not have the same probability of being included in the sample.

What is an example of Random Sampling given in the text?

The teacher asking students to write their names on a piece of paper, placing them in a box, and then randomly choosing a student for an oral recitation.

What are the different types of Non-Random Sampling mentioned in the text?

Convenience Sampling, Quota Sampling, Purposive Sampling, Snowball Sampling

What is Slovin's Formula used for?

To calculate the sample size needed based on the population size and the margin of error. Signup and view all the answers

What are the components of Slovin's Formula?

n = Sample size, N = Population size, e = Margin of error Signup and view all the answers

In the given example, what is the sample size required for a population of 2,000 with a 97% confidence level?

123 Signup and view all the answers

What is a probability distribution of a discrete random variable?

A list, a table, a graph, or a formula showing all the possible values of a discrete random variable together with their corresponding properties. Signup and view all the answers

What should be the range of all probabilities in a probability distribution?

Between 0 and 1, inclusive. Signup and view all the answers

How is the mean of a discrete random variable defined?

The expected value of X, also referred to as the mean of X. Signup and view all the answers

What do the variance and standard deviation describe in a probability distribution?

The dispersion or the variability of the distribution. Signup and view all the answers

What is the formula for computing the variance of a discrete random variable?

The variance can be computed using the formula. Signup and view all the answers

What is the relationship between the sum of all probabilities in a probability distribution and the value 1?

The sum of all probabilities in a probability distribution should be equal to 1. Signup and view all the answers

What is simple random sampling?

A subset of individuals from a larger population chosen so that every individual has an equal chance of being selected. Signup and view all the answers

Why is defining the population important in simple random sampling?

To clearly identify the group of people, objects, or events with similar characteristics that you want to study. Signup and view all the answers

What is a sampling frame?

A list of all the individuals or items in the population from which the sample will be selected. Signup and view all the answers

How do you determine the sample size in simple random sampling?

By deciding on the size of the sample needed to draw meaningful conclusions. Signup and view all the answers

What is the final step in simple random sampling after collecting data?

Analyzing the collected data using appropriate statistical methods. Signup and view all the answers

What is a key advantage of simple random sampling in terms of representation?

Unbiased representation, where every member of the population has an equal chance of being selected. Signup and view all the answers

What is a random experiment?

An experiment that can be repeated numerous times under the same conditions with independent results. Signup and view all the answers

Define outcome in the context of a random experiment.

The result of a random experiment. Signup and view all the answers

Explain what a sample space is.

The set of possible outcomes of a random experiment. Signup and view all the answers

What is a random variable?

A function that associates a numerical value to every outcome of a random experiment. Signup and view all the answers

Differentiate between a discrete and a continuous random variable.

Discrete random variables have a finite or countably infinite number of values, while continuous random variables can assume an infinite number of values, including decimal or fractional values. Signup and view all the answers

Give an example of a discrete random variable.

The number of phones produced by a company. Signup and view all the answers

What is the purpose of using Two-Stage Sampling?

To avoid prejudice and obtain representative data Signup and view all the answers

Describe the process of Multi-Stage Sampling.

Each selected cluster is subjected to additional sample in addition to the first cluster sampling. Signup and view all the answers

In the example provided of conducting a customer survey, what is the chosen cluster for selection?

Age Groups Signup and view all the answers

What is the purpose of conducting Stratified Sampling?

To break a population into smaller groups based on common features or attributes. Signup and view all the answers

Why is Stratified Sampling considered to be more complex than simple random sampling?

Because it involves breaking the population into smaller groups (strata) based on certain characteristics. Signup and view all the answers

What is the key difference between Two-Stage Sampling and Multi-Stage Sampling?

Two-Stage Sampling selects a subsample cluster from the selected, while Multi-Stage Sampling adds additional samples to each selected cluster. Signup and view all the answers