Question 1

Which of the following best defines a 'parameter' in statistics?

Accepted Answer

A characteristic, usually numerical, describing a population.

Question 2

In the research question 'Does smoking affect lung capacity?', which is the explanatory variable?

Accepted Answer

Smoking

Question 3

A group of students surveys people at a local mall to study health differences between wealthy and low-income individuals. What type of sampling method is this?

Accepted Answer

Convenience sampling

Question 4

Which of the following is most likely to be a confounding variable in a study examining the relationship between income and health?

Accepted Answer

Age of participants

Question 5

What is the main risk of using a convenience sample, such as surveying only people at a mall?

Accepted Answer

It may not represent the entire population, leading to bias.

Question 6

Suppose a statistician wants to estimate the average height of all university students. She measures the height of 100 randomly selected students. In this context, what is the 'statistic'?

Accepted Answer

The average height of the 100 selected students.

Question 7

Which of the following best describes a 'sample frame'?

Accepted Answer

The set of all individuals in the population that could be included in the sample.

Question 8

A researcher is interested in whether exercise improves memory. She randomly assigns participants to two groups: one that exercises daily and one that does not. She then measures memory performance. What is the response variable?

Accepted Answer

Memory performance

Question 9

Which of the following scenarios best illustrates the concept of a confounding variable?

Accepted Answer

A study finds a correlation between ice cream sales and drowning incidents, but temperature is not considered.

Question 10

In the mall survey example, which segment of the population is most likely to be underrepresented?

Accepted Answer

People who do not visit malls

Question 11

If a study's research question is 'Is there an association between diet and heart disease?', which of the following is most likely the explanatory variable?

Accepted Answer

Diet

Question 12

A sample is best described as:

Accepted Answer

A subset of the population.

Question 13

Which of the following is an example of a biased sampling method?

Accepted Answer

Surveying only people who are easily accessible to the researcher.

Question 14

Suppose you want to study the effect of a new teaching method on student performance. Which of the following would be a confounding variable if not controlled?

Accepted Answer

Prior knowledge of students

Question 15

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter describes a population, while a statistic describes a sample.

Question 16

A researcher wants to know if a new drug lowers blood pressure. She measures blood pressure before and after administering the drug. What is the response variable?

Accepted Answer

Blood pressure

Question 17

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

Accepted Answer

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

Question 18

A study finds that people who exercise more tend to have lower stress levels. Which of the following could be a confounding variable in this study?

Accepted Answer

Diet quality

Question 19

In the context of the mall survey, which of the following is a plausible reason for bias in the sample?

Accepted Answer

People at malls may not represent the income distribution of the entire population.

Question 20

Which of the following best describes an explanatory variable?

Accepted Answer

A variable that is manipulated or categorized to observe its effect on the response variable.

Chapter 1: Collecting Data – Sampling Methods in Statistics

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