Q: Which formula would you use to calculate the probability of an event occurring by chance, relevant to statistical significance?

$$P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$

Question 1

Which of the following best describes the difference between a population and a sample in statistics?

Accepted Answer

A population is the complete collection of data or subjects under consideration, while a sample is a subcollection of members selected from the population.

Question 2

In a survey conducted by a magazine where readers voluntarily register their responses online, what is the main issue with this sampling method?

Accepted Answer

The sample is a voluntary response sample, so the results may not reflect the opinions of the general population.

Question 3

Which of the following is an example of a census?

Accepted Answer

Collecting data from every household in a city for a government population count.

Question 4

A researcher posts a survey online asking, 'Have you ever been affected by a computer virus?' and receives 10,000 responses. What type of sampling method is this?

Accepted Answer

Voluntary response sampling

Question 5

Which of the following best defines statistical significance?

Accepted Answer

A result is considered statistically significant if the likelihood of it occurring by chance is 5% or less.

Question 6

In a study, a new diet program resulted in an average weight loss of 22 pounds among 40 subjects, with about a 1% chance of getting such results from a program that has no effect. Which type of significance is achieved?

Accepted Answer

Statistical significance

Question 7

Which of the following is NOT a step in the process of statistical and critical thinking as described in the study materials?

Accepted Answer

Guess: Make assumptions without data

Question 8

A survey question is worded as, 'Don’t you agree that recycling is essential for saving the planet?' What is the main issue with this question?

Accepted Answer

It is a loaded question, intentionally worded to elicit a desired response.

Question 9

Which of the following scenarios best illustrates practical significance without statistical significance?

Accepted Answer

A new teaching method improves test scores by 15 points, but the improvement is not statistically significant.

Question 10

Suppose you want to estimate the average height of all university students. You measure the heights of 200 randomly selected students. What is the population and what is the sample?

Accepted Answer

Population: All university students; Sample: 200 students measured

Question 11

Which formula would you use to calculate the probability of an event occurring by chance, relevant to statistical significance?

Accepted Answer

$$P = \frac{	ext{Number of favorable outcomes}}{	ext{Total number of possible outcomes}}$$

Question 12

A study finds a statistically significant difference in test scores between two teaching methods, but the difference is only 0.5 points. What should be considered before recommending the new method?

Accepted Answer

Whether the difference is practically significant and justifies changing teaching methods.

Question 13

Which of the following is most likely to introduce bias into a survey?

Accepted Answer

Using a voluntary response sample.

Question 14

In the context of statistical studies, what does 'context' refer to?

Accepted Answer

The background information and circumstances surrounding the data collection.

Question 15

Which of the following is a critical step in analyzing data according to the statistical thinking process?

Accepted Answer

Graphing the data to visualize patterns.

Question 16

A survey asks, 'Do you support the new law that will protect children from harmful content?' What is the main problem with this question?

Accepted Answer

It is a loaded question designed to elicit a positive response.

Question 17

Which of the following best describes the science of statistics?

Accepted Answer

The science of planning studies and experiments, obtaining data, organizing, summarizing, presenting, analyzing, and interpreting those data, and drawing conclusions based on them.

Question 18

If a survey is conducted only among people who choose to respond, which of the following is most likely true?

Accepted Answer

The results may be biased toward those with strong feelings about the issue.

Question 19

Which of the following is NOT a reason why voluntary response samples can be problematic?

Accepted Answer

They always use random sampling.

Statistics and Critical Thinking: Foundations and Applications

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