Q: In a survey, 60% of 500 respondents said they use public transportation. Of those, 40% are students. How many students use public transportation according to the survey?

$$500 \times 0.60 \times 0.40 = 120$$

Question 1

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

Accepted Answer

A sample is a subset of the population from which data are obtained, while a population is the complete set of people or objects being studied.

Question 2

A researcher collects data on the number of hours students study per week and their declared major. Which variable is numerical and which is categorical?

Accepted Answer

Number of hours is numerical; major is categorical.

Question 3

A study finds that people who eat more vegetables tend to have lower cholesterol. Which of the following is the most accurate statement about this finding?

Accepted Answer

There is an association between eating more vegetables and lower cholesterol, but causation cannot be inferred without a controlled experiment.

Question 4

Which of the following is an example of a confounding variable in a study examining the relationship between exercise and weight loss?

Accepted Answer

The amount of sleep participants get each night.

Question 5

A pharmaceutical company wants to test a new drug. They randomly assign 200 patients to receive either the drug or a placebo, and neither the patients nor the doctors know who receives which. What type of study is this?

Accepted Answer

Double-blind controlled experiment

Question 6

In a survey, 60% of 500 respondents said they use public transportation. Of those, 40% are students. How many students use public transportation according to the survey?

Accepted Answer

$$500 	imes 0.60 	imes 0.40 = 120$$

Question 7

Which of the following best explains why rates (such as per 1,000 people) are often more useful than raw counts when comparing groups of different sizes?

Accepted Answer

Rates allow for direct comparison by accounting for differences in group sizes.

Question 8

A study reports that 20 out of 100 patients who received a new treatment recovered, while 10 out of 100 in the control group recovered. What is the recovery rate for the treatment group?

Accepted Answer

$$\frac{20}{100} = 0.20 = 20\%$$

Question 9

Which of the following statements about anecdotal evidence is correct?

Accepted Answer

Anecdotal evidence should not be used to make general statements about groups.

Question 10

A frequency table is used to:

Accepted Answer

Display the distribution of a categorical variable by showing the count of each category.

Question 11

In a two-way table summarizing the results of a survey on gender (male/female) and seatbelt use (always/not always), which cell would represent the number of women who do not always wear a seatbelt?

Accepted Answer

The cell at the intersection of 'female' and 'not always'.

Question 12

A researcher wants to know if a new teaching method improves test scores. She assigns students to groups based on their previous grades, with higher-performing students in the new method group. What type of bias is most likely present?

Accepted Answer

Selection bias due to non-random assignment.

Question 13

Which of the following is a key feature of a double-blind experiment?

Accepted Answer

Neither the participants nor the researchers know who is in the treatment or control group.

Question 14

A study finds a strong association between ice cream sales and drowning incidents. Which of the following is the best explanation for this association?

Accepted Answer

A confounding variable, such as temperature, affects both ice cream sales and drowning incidents.

Question 15

Which of the following best describes a categorical variable?

Accepted Answer

A variable that describes qualities or group membership, such as eye color or type of car.

Question 16

A city has 1,000,000 residents and reports 2,500 cases of a certain disease. What is the rate of disease per 1,000 residents?

Accepted Answer

$$\frac{2,500}{1,000,000} 	imes 1,000 = 2.5$$

Question 17

In a controlled experiment, why is random assignment of subjects to treatment and control groups important?

Accepted Answer

It helps ensure that differences between groups are due to the treatment and not other factors.

Question 18

A study on the effect of a new fertilizer on plant growth assigns plants to treatment and control groups by flipping a coin. After 8 weeks, the treatment group has a mean height of 15 cm and the control group has a mean height of 12 cm. Which conclusion is most justified?

Accepted Answer

The new fertilizer likely causes increased plant growth, since random assignment allows for causal inference.

Question 19

Which of the following is NOT a characteristic of the 'gold standard' for experiments?

Accepted Answer

Small sample size.

Question 20

A researcher codes 'Yes' as 1 and 'No' as 0 for a survey question. What type of variable is this, and why might this coding be used?

Accepted Answer

Categorical variable; coding makes data entry and analysis easier.

Chapter 1: Introduction to Data – Essential Concepts in Statistics

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