Understanding Proportions and Percentages

The video tutorial explains the concept of random sampling and its importance in making population inferences. It highlights the need for fairness in sampling, ensuring every individual has an equal chance of selection. Through examples, it distinguishes between fair and unfair sampling methods. The tutorial also demonstrates how to use sample data to infer about the entire population using proportions and percentages, with practical problems like a library survey to illustrate these concepts.

What is the main goal of random sampling?

• To survey every individual in a population

• To ensure a fair representation of a population

• To exclude certain groups from the survey

• To focus only on a specific group within a population

Which of the following is an example of a fair random sample?

• Asking only students who bring home lunch

• Surveying only students who take the bus

• Asking every 20th person in a lunchroom

• Surveying only the girls in a lunch line

Why is it important for everyone in a population to have an equal chance of being selected?

• To focus on a specific group

• To make the survey more interesting

• To ensure the survey is quick

• To avoid bias in the results

How do you set up a proportion to infer data from a sample to a whole population?

• By using only the total population data

• By ignoring the total population

• By setting up two equal fractions

• By using only the sample data

In the example of the Internet company, what was the purpose of setting up a proportion?

• To identify the least used internet service

• To calculate the average internet usage

• To determine how many customers use the internet more than 15 hours per week

• To find out the total number of customers

What is the first step in solving a problem using proportions?

• Add all the numbers together

• Cross-multiply the numbers

• Set up a proportion with part-to-whole relationships

• Divide the total by the sample size

In the library example, how many patrons can be expected to choose a science fiction book?

• 125

• 100

• 75

• 50

What percentage of library patrons chose a mystery book?

• 55%

• 45%

• 42%

• 50%

How do you convert a fraction to a percentage?

• Subtract 100 from the fraction

• Add 100 to the fraction

• Divide the fraction by 100

• Multiply the fraction by 100

What is the percentage of patrons who chose a nonfiction book?

• 35%

• 30%

• 25%

• 20%