Q: Which formula is commonly used to calculate the margin of error for a sample proportion?

$\text{Margin of Error} = 2 \times \sqrt{\frac{p(1-p)}{n}}$

Question 1

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

Accepted Answer

Descriptive statistics summarize and present data, while inferential statistics use sample data to make predictions or decisions about a population.

Question 2

A researcher wants to estimate the average height of all university students. She measures the height of 200 randomly selected students. In this context, what is the population?

Accepted Answer

All university students.

Question 3

In a poll of 1,000 voters, 60% said they support a new environmental law. Which term best describes the 60% figure?

Accepted Answer

Sample statistic

Question 4

Which of the following is an example of a statistical question?

Accepted Answer

How many students in this class own a smartphone?

Question 5

A study finds that 77% of 3,250 walk buttons at traffic intersections in New York City do not work. Is the figure 77% a parameter or a statistic?

Accepted Answer

Parameter, because it describes the entire population of walk buttons.

Question 6

Which of the following best illustrates the concept of 'margin of error' in survey results?

Accepted Answer

The range within which the true population percentage is likely to fall, based on the sample result.

Question 7

Suppose a poll of 929 New York residents finds that 48% support a ban on plastic bags, with a margin of error of 4.1%. What is the interval in which the true population percentage is likely to fall?

Accepted Answer

$48\% \pm 4.1\%$; that is, between $43.9\%$ and $52.1\%$

Question 8

Which of the following is NOT a component of the statistical investigative process?

Accepted Answer

Ignore outliers

Question 9

Why is randomness important in statistical sampling?

Accepted Answer

It allows for unbiased inferences about the population.

Question 10

A pharmaceutical company tests a new drug on a random sample of 500 patients and finds that 65% show improvement. What is the population parameter in this scenario?

Accepted Answer

The percentage of all patients who would show improvement if given the drug.

Question 11

Which formula is commonly used to calculate the margin of error for a sample proportion?

Accepted Answer

$	ext{Margin of Error} = 2 	imes \sqrt{\frac{p(1-p)}{n}}$

Question 12

Which of the following scenarios best illustrates 'between sample variability'?

Accepted Answer

Two different samples from the same population produce different average heights.

Question 13

A TV advertisement for a new coffee product is followed by a 30% increase in sales over three months. What is a major flaw in concluding that the advertisement was effective?

Accepted Answer

The increase in sales may be due to other factors not accounted for.

Question 14

Which of the following is an example of a population parameter?

Accepted Answer

The average graduation rate of all colleges in the US in 2019-2020.

Question 15

Why is it important to question statistical claims encountered in everyday life?

Accepted Answer

Because the interpretation or source of the statistics may be flawed or deceptive.

Question 16

In a study, the subjects are defined as:

Accepted Answer

The entities that are measured in the study.

Question 17

Which of the following best describes the role of probability in statistics?

Accepted Answer

Probability provides a framework for quantifying how likely various possible outcomes are.

Question 18

A sample of 877 executives is surveyed, and 45% say they would not hire someone with a typographical error on their job application. What is the sample in this scenario?

Accepted Answer

The 877 executives surveyed.

Question 19

Which of the following is a key reason for using statistical methods in research?

Accepted Answer

To collect, summarize, and interpret data to answer investigative questions.

(Lecture 1) Introduction to Statistics: Data, Populations, and Statistical Reasoning

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