Analyzing Samples

Imagine a study is conducted at a university to determine the average number of textbooks a group of engineering students reads over the course of a semester. Which of the following factors would most likely increase the precision of the sampling distribution of the sample mean?

• Decreasing the sample size

• Increasing the variability of the number of textbooks read

• Increasing the sample size

• Using a convenience sample instead of a random sample

Imagine a researcher is interested in estimating the average height of plants in a large botanical garden. To achieve this, they decide to take samples from different sections of the garden. What is the primary reason for using the sampling distribution of the sample mean in this scenario?

• To directly measure the height of every plant in the garden

• To estimate the average height of plants in the entire garden from the sample means

• To prove that the sampled plants are taller than the rest

• To show that sampling is unnecessary in large populations

In a high school of 1,000 students, analyzing the test scores of 100 random students creates what type of distribution?

• Sampling distribution

• Population distribution

• Sample distribution

• Frequency distribution

In statistical analysis, which distribution type requires multiple samples of the same size?

• Sample distribution

• Population distribution

• Sampling distribution

• Standard distribution

What is the difference between a sample and a population?

A ​ (a)   is a set of all items or events which are of interest for some question or experiment.

It is generally the group you are trying to make predictions or learn something about.

For most studies, it is either impossible or impractical to obtain data on an entire population.

This is why you need to use a smaller selection of items.

A ​ (b)   is a selection of observations from a population.

We measure data in a known sample to make a prediction, or inference, about the population.

• population

• correlation

• sample

• causation

• ideation

• application

• understudy

• sample survey

• experiment

• observational study

What is a key limitation of using a sample distribution?

• It represents the entire population

• It may not perfectly reflect population characteristics

• It requires too many measurements

• It can only use certain graph types

A researcher wants to understand how sample statistics vary across multiple samples. Which distribution should they use?

• Sample distribution

• Normal distribution

• Population distribution

• Sampling distribution

Which characteristic best describes a sample distribution?

• Shows all possible population values

• Represents multiple sample means

• Includes every member of the group

• Represents a fraction of the population

Which distribution helps in estimating population parameters without studying every individual?

• Frequency distribution

• Sample distribution

• Sampling distribution

• Population distribution

If you want to study a large group of people, but it's impractical to collect data from everyone, what method might you use to select a smaller group to represent the whole?

• Census

• Random sample

• Systematic sample

• Population