Question 1

Which of the following best describes the difference between descriptive and inferential statistics?

Accepted Answer

Descriptive statistics summarize and visualize data, while inferential statistics use data to make generalizations about a population.

Question 2

A pharmaceutical company tests a new drug on a group of 500 patients and finds an average recovery time of 8 days. The company wants to know the average recovery time for all patients who might use the drug. In this scenario, what is the parameter?

Accepted Answer

The average recovery time for all patients who might use the drug.

Question 3

Which of the following is an example of a statistic?

Accepted Answer

The mean test score of a random sample of 100 students from a university.

Question 4

Suppose a researcher wants to estimate the average number of hours college students sleep per night. She surveys 200 students from her university. What is the population in this study?

Accepted Answer

All college students.

Question 5

Which of the following best defines 'variability' in the context of statistics?

Accepted Answer

Natural fluctuation in data from case to case or study to study.

Question 6

A company wants to know the average battery life of all batteries it produces. It tests 50 batteries from today's production line and finds an average life of 16.7 hours. What is the statistic in this scenario?

Accepted Answer

The average battery life of 16.7 hours from the 50 tested batteries.

Question 7

Which of the following is an example of bias in a statistical study?

Accepted Answer

Consistently overestimating the average income due to surveying only high-income neighborhoods.

Question 8

In the context of sampling, what is the 'sampling frame'?

Accepted Answer

The list or mechanism from which the sample is drawn.

Question 9

Which of the following statements about parameters and statistics is correct?

Accepted Answer

A parameter is a numerical summary of a population, while a statistic is a numerical summary of a sample.

Question 10

A streaming service tests two home page designs on 5,000 visitors each. Version B produces a 0.6 percentage-point higher click-through rate than Version A. What type of statistical method would you use to decide if this difference is meaningful?

Accepted Answer

Inferential statistics

Question 11

Which of the following best describes a 'sample' in statistics?

Accepted Answer

A subset of the population that is actually observed and analyzed.

Question 12

A researcher wants to study the average commute time for all employees at a large company. She randomly selects 100 employees and records their commute times. Which of the following is the observational unit?

Accepted Answer

Each individual employee.

Question 13

Which of the following is an example of inferential statistics?

Accepted Answer

Using a sample of 200 voters to estimate the proportion of all voters who support a candidate.

Question 14

Why is it important to distinguish between a population and a sample in statistical studies?

Accepted Answer

Because we use statistics from samples to estimate parameters of populations.

Question 15

Which of the following best describes 'bias' in a statistical context?

Accepted Answer

A systematic deviation in design, measurement, or selection that pushes results in a consistent direction.

Question 16

A researcher collects data on the heights of 100 randomly selected high school students to estimate the average height of all high school students in the country. Which of the following is the parameter?

Accepted Answer

The average height of all high school students in the country.

Question 17

Which of the following is a reason why sampling might not work well in a study?

Accepted Answer

If the sample is not representative of the population.

Question 18

Suppose you want to estimate the average number of hours spent studying per week by all university students. You survey 300 students from your university. Which of the following is the accessible population?

Accepted Answer

All students at your university.

Question 19

Which of the following equations correctly represents the sample mean $\bar{x}$ for a set of $n$ observations $x_1, x_2, ..., x_n$?

Accepted Answer

$\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i$

Question 20

A dartboard analogy is often used to explain variability and bias. Which of the following best matches this analogy?

Accepted Answer

Variability is like darts landing all around the bullseye at random; bias is like darts consistently landing off to one side.

Foundations of Statistics: Concepts, Populations, and Samples

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