1. you are surveying students to find out their opinion of the quality of food on the cafeteria. you decide to poll only those students who buy a hot lunch on a particular day. is your sample random? please explain!

2. a researcher tagged 40 giant turtles in 2008. In 2009, she returned and captured 50 turtles 16 of which were tagged. in 2010 she returned again and captured 30 turtles, 8 of which were tagged.
A. use a proportion to estimate the turtle population for 2009
B. use a proportion to estimate the turtle population for 2010

A random sample is a subset of a statistical population where "each subset member has the same probability of being picked". A random sample is meant to accurately reflect a group of people.

Key takeaways:

A random sample represents the "complete data set by selecting a tiny, random portion of the total population, with each member having an equal chance of being chosen".
Using procedures such as lotteries or random draws, researchers can generate a random sample.
A sampling mistake can occur with a simple random sample if the sample does not accurately reflect the population it is meant to represent.

Example:

In a firm with 250 employees, a simple random sample may consist of the names of 25 employees selected from a hat. In this scenario, the population is all 250 employees, and the sample is random since each employee has an equal chance of being chosen.

Random sampling is used in science to conduct blinded studies or randomized control testing.

This sample cannot be called a random sample. This is because a "random sample is an unbiased representation of the group and here we have not taken the opinions of the students who don’t eat hot lunch". So this sample can’t be a random one.

Learn more about random sample here:

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2.

The Turtle population for 2009 comes out to be 125.

The Turtle Population for 2010 comes out to be 150.

What is Proportion?

A mathematical comparison of two numbers is referred to as a proportion. According to proportion, "two sets of provided numbers that rise or decrease in the same ratio are considered to be directly proportionate to each other".

The sign "::" or "=" is used to represent proportions.

When two ratios are equal, they are said to be in proportion. For example, the time it takes a train to go 100 kilometers per hour is the same as the time it takes to travel 500 kilometers in 10 hours. For example, 100 km/hr = 500 km/10 hours.

For 2009, we are going to calculate the percentage population that was tagged

So, this comes out to be

16÷50×100

⇒32 percent

So the population now becomes 40÷(32÷100)

⇒40×100÷32

⇒125 Turtles

Similarly for 2010,

Percentage population tagged = 8×100÷30

⇒26.7 percent

So the population becomes,

40÷(26.7)

⇒150 Turtles

Learn more about proportion here,

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