Q: Suppose you want to select a simple random sample of 2 officials from a population of 5: Governor (G), Lieutenant Governor (L), Secretary of State (S), Attorney General (A), and Treasurer (T). How many possible samples of size 2 can be drawn without replacement?

$$ \frac{5!}{2! \times 3!} = 10 $$

Q: Which of the following R commands will randomly select 3 individuals from a dataset called ECON103_Names without replacement?

$$ \text{sample(ECON103\_Names, 3, replace = FALSE)} $$

Question 1

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

Accepted Answer

Descriptive statistics summarize and organize data, while inferential statistics draw conclusions about a population based on sample data.

Question 2

A coffee shop owner surveys 300 residents about their coffee preferences and concludes that including all varieties will bring more customers. What type of statistics is being used in making this conclusion?

Accepted Answer

Inferential statistics, because the owner is making a prediction about the entire population based on the sample.

Question 3

Which of the following is an example of descriptive statistics?

Accepted Answer

Calculating the mean and median ratings of movies released between 1990 and 2020.

Question 4

Suppose you want to select a simple random sample of 2 officials from a population of 5: Governor (G), Lieutenant Governor (L), Secretary of State (S), Attorney General (A), and Treasurer (T). How many possible samples of size 2 can be drawn without replacement?

Accepted Answer

$$ \frac{5!}{2! 	imes 3!} = 10 $$

Question 5

In the context of simple random sampling, what does it mean for each possible sample to be 'equally likely'?

Accepted Answer

Each possible group of the specified sample size has the same probability of being chosen.

Question 6

A pollster wants to estimate the proportion of U.S. adults who support a new policy. She randomly selects 1,000 adults and finds that 60% support the policy. Which formula should she use to estimate the standard error of the sample proportion?

Accepted Answer

$$ \sqrt{\frac{p(1-p)}{n}} $$

Question 7

Which of the following scenarios best illustrates inferential statistics?

Accepted Answer

Using a sample of 500 voters to predict the outcome of a national election.

Question 8

If you use a random number generator to select 10 numbers between 1 and 40 without replacement, what is the probability that any particular number is selected in the sample?

Accepted Answer

$$ \frac{10}{40} = 0.25 $$

Question 9

A researcher wants to know the social media preference of the entire ECON103 class. She surveys every student in the class. Is this study descriptive or inferential?

Accepted Answer

Descriptive, because she is summarizing data from the entire population of interest.

Question 10

Which of the following is NOT a requirement for a simple random sample?

Accepted Answer

The sample must be larger than the population.

Question 11

In a survey, 100% of adults reported liking Americano coffee. If this result is only from the sample, what type of error might occur when generalizing to the population?

Accepted Answer

Sampling error, because the sample may not represent the entire population.

Question 12

Which of the following R commands will randomly select 3 individuals from a dataset called ECON103_Names without replacement?

Accepted Answer

$$ 	ext{sample(ECON103\_Names, 3, replace = FALSE)} $$

Question 13

A public opinion poll is conducted using a sample of 1,000 voters to estimate the preferences of all U.S. voters. What is the population in this study?

Accepted Answer

All U.S. voters.

Question 14

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

Accepted Answer

It helps to obtain a sample that is representative of the population, reducing bias.

Question 15

Given the following movie ratings: 9.3, 9.2, 9.0, 8.9, 8.8, what is the median rating?

Accepted Answer

$$ 9.0 $$

Question 16

If a sample is not representative of the population, which of the following is most likely to occur?

Accepted Answer

The results may be biased and not generalizable to the population.

Question 17

Which of the following is a valid reason for using a random number generator in sampling?

Accepted Answer

To eliminate human bias in the selection process.

Question 18

A poll is performed on 10 students randomly selected from a class. The results are used to estimate the preferences of the entire class. Is this study descriptive or inferential?

Accepted Answer

Inferential, because it uses sample data to make conclusions about the population.

Question 19

Which of the following is NOT an example of descriptive statistics?

Accepted Answer

Using a sample to predict the outcome of a future event.

Chapter 1: The Nature of Statistics – Descriptive Statistics, Inferential Statistics, and Simple Random Sampling

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