Question 1

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

Accepted Answer

Descriptive statistics summarize and describe the main features of a dataset, while inferential statistics use data from a sample to make generalizations about a population.

Question 2

Suppose a researcher wants to estimate the average height of all university students. She randomly selects 100 students and calculates their average height. In this scenario, what is the sample and what is the population?

Accepted Answer

The 100 students are the sample; all university students are the population.

Question 3

Which of the following is an example of using inferential statistics?

Accepted Answer

Estimating the proportion of voters who support a candidate based on a survey of 1,000 voters.

Question 4

Which of the following statements about probability models in statistics is correct?

Accepted Answer

Probability models help us understand the uncertainty associated with making inferences from a sample to a population.

Question 5

John Graunt estimated the population of London in the 17th century by using mortality tables. Which assumption did he implicitly make in his estimation?

Accepted Answer

That the proportion of deaths in his sample was representative of the entire population.

Question 6

Which of the following best explains why random sampling is important in statistics?

Accepted Answer

It allows us to make unbiased inferences about the population from the sample.

Question 7

A researcher wants to know the average number of hours students study per week. She surveys 200 students and finds a mean of 15 hours. Which statistical concept allows her to estimate the average for all students at the university?

Accepted Answer

Inferential statistics

Question 8

Which of the following is NOT a characteristic of a good sample in statistics?

Accepted Answer

It is chosen based on convenience.

Question 9

Suppose you want to estimate the proportion of defective items produced by a factory. Which of the following sampling methods is most likely to yield a representative sample?

Accepted Answer

Randomly selecting items from the entire production line.

Question 10

Which of the following historical figures is credited with laying the foundation for modern inferential statistics by developing probability theory?

Accepted Answer

Pierre-Simon Laplace

Question 11

A sample mean is calculated as $$ \bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i . $$What does $$ n $$ represent in this formula?

Accepted Answer

The number of observations in the sample

Question 12

Which of the following best describes the main purpose of descriptive statistics?

Accepted Answer

To summarize and present the main features of a dataset

Question 13

Suppose a mortality table shows that 8 out of 100 people die before age 10. What proportion survives to at least age 10?

Accepted Answer

$$0.92$$

Question 14

Which of the following is a key insight from Halley's work on mortality tables?

Accepted Answer

Mortality rates vary with age, and life insurance premiums should depend on the age of the person being insured.

Question 15

Which of the following is an example of a population in statistics?

Accepted Answer

All students in a university

Question 16

If a sample is not representative of the population, what is the most likely consequence?

Accepted Answer

Inferences made about the population may be biased or incorrect.

Question 17

Which of the following best describes the historical development of statistics?

Accepted Answer

Statistics began as a tool for summarizing census data and evolved to include probability theory and inferential methods.

Question 18

A researcher uses the formula $$ s^2$ = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2$  to $$calculate the variance of a sample. What does $$ s^2$ $$ represent?

Accepted Answer

The sample variance

Question 19

Which of the following is a reason why probability models are important in inferential statistics?

Accepted Answer

They allow us to describe the uncertainty associated with estimates based on samples.

Introduction to Statistics: Populations, Samples, and Descriptive Statistics

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