Q: A researcher wants to estimate the proportion of students who use seatbelts. Which formula should be used to calculate the sample proportion $$\hat{p}$$?

$$\hat{p} = \frac{\text{Number of students who use seatbelts}}{\text{Total number of students in sample}}$$

Question 1

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

Accepted Answer

A population is the entire group of interest, while a sample is a subset selected from the population.

Question 2

In a study investigating the effect of a new drug on blood pressure, which variable is most likely the response variable?

Accepted Answer

The blood pressure measured after treatment.

Question 3

A researcher wants to study the relationship between gender and seatbelt usage. Which type of table would best summarize the frequency of seatbelt usage by gender?

Accepted Answer

A two-way (contingency) table.

Question 4

Which of the following is a categorical variable?

Accepted Answer

Type of car (sedan, SUV, truck)

Question 5

Suppose a survey asks: 'Do you always wear a seatbelt?' and records responses as 'Always' or 'Not Always'. If 7 females and 3 males respond 'Always', what is the relative frequency of females who always wear seatbelts in a sample of 15 people (7 females, 8 males)?

Accepted Answer

$$\frac{7}{15}$$

Question 6

Which of the following best describes a double-blind study?

Accepted Answer

Neither the subjects nor the researchers know which group receives the treatment.

Question 7

A simple random sample is characterized by which property?

Accepted Answer

Each individual in the population has an equal chance of being selected.

Question 8

In the context of the Old Faithful geyser example, which variable is most likely to be considered numerical?

Accepted Answer

Length of eruption (in minutes)

Question 9

Which of the following is an example of an observational study?

Accepted Answer

A researcher collects data on seatbelt usage without intervening.

Question 10

A frequency table is used to:

Accepted Answer

Display all possible outcomes for a variable and how often each occurs.

Question 11

Which of the following is NOT a step in the statistical investigation process (data cycle)?

Accepted Answer

Ignore the Data

Question 12

In a controlled experiment, what is the main purpose of the control group?

Accepted Answer

To provide a baseline for comparison with the treatment group.

Question 13

If a study finds that students who sleep more tend to have higher test scores, but does not assign sleep amounts, what type of study is this?

Accepted Answer

Observational study

Question 14

Which of the following is a numerical variable?

Accepted Answer

Number of doors on a car

Question 15

A researcher wants to estimate the proportion of students who use seatbelts. Which formula should be used to calculate the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{	ext{Number of students who use seatbelts}}{	ext{Total number of students in sample}}$$

Question 16

Which of the following best describes the placebo effect?

Accepted Answer

Subjects experience changes because they believe they are receiving treatment, even if they are not.

Question 17

In a study, the variable 'weight' is measured in kilograms. What type of variable is 'weight'?

Accepted Answer

Numerical

Question 18

A researcher collects data on the number of doors, weight, and head injury numbers for different car models. Which of these variables is categorical?

Accepted Answer

Car model

Question 19

Which sampling method is most likely to introduce bias?

Accepted Answer

Convenience sampling

Question 20

Suppose you want to know if a new vaccine reduces the risk of contracting a disease. You randomly assign participants to receive the vaccine or a placebo and follow up to see who contracts the disease. What type of study is this?

Accepted Answer

Controlled experiment

Introduction to Statistics: Exam 1 Study Notes (Lectures 1–6)

Study Guide - Practice Questions

Study Guide - Flashcards