Q: If the mean of three exam scores is 84.3, which formula was used to calculate this mean?

$$\text{Mean} = \frac{\text{Sum of all scores}}{\text{Number of scores}}$$

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 individuals to be studied, while a sample is a subset of that group.

Question 2

A tire manufacturer finds that the number of miles their tires last before blow-out is normally distributed with mean $$\mu = 60,000$$ miles and standard deviation $$\sigma = 4,000$$ miles. If they warrant their tires for 52,000 miles, what percentage of tires would be expected to blow out while still under warranty?

Accepted Answer

About 16%

Question 3

Which of the following is an example of a parameter?

Accepted Answer

The average number of points earned per student over all math classes at a university.

Question 4

Suppose you want to estimate the mean plaque level in a population using a new toothpaste additive. You want a 95% confidence level and a margin of error less than 0.2. Which formula would you use to determine the minimum sample size needed?

Accepted Answer

$$n = \left( \frac{z^* \cdot \sigma}{E} \$$right)^2$$

Question 5

Which of the following variables is best classified as a discrete quantitative variable?

Accepted Answer

Number of siblings

Question 6

A survey of 1,013 adults in the United States found that 66% worried about identity theft. In this context, what is the sample?

Accepted Answer

The 1,013 adults surveyed

Question 7

Which of the following best describes a categorical (qualitative) variable?

Accepted Answer

A variable that places individuals into categories or groups

Question 8

If the mean of three exam scores is 84.3, which formula was used to calculate this mean?

Accepted Answer

$$	ext{Mean} = \frac{	ext{Sum of all scores}}{	ext{Number of scores}}$$

Question 9

Which of the following is an example of an ordinal variable?

Accepted Answer

Student's grade in a course (A, B, C, D, F)

Question 10

A researcher collects data on the time (in hours) students spend studying per week. What type of variable is this?

Accepted Answer

Quantitative, continuous

Question 11

Which of the following statements about probability is correct?

Accepted Answer

Probability is a mathematical tool used to study randomness and the likelihood of events.

Question 12

Which of the following best describes a census?

Accepted Answer

A collection of data from every individual of a population.

Question 13

Which of the following is a correct interpretation of the 68-95-99.7 rule for a normal distribution?

Accepted Answer

About 68% of the data falls within one standard deviation of the mean.

Question 14

Which of the following is NOT a characteristic of a quantitative variable?

Accepted Answer

It places individuals into categories.

Question 15

A researcher wants to know the average height of all students at a university. She measures the height of 100 randomly selected students. In this context, what is the statistic?

Accepted Answer

The average height of the 100 students measured.

Question 16

Which of the following is an example of a nominal variable?

Accepted Answer

Name of a city

Question 17

If a variable can take on any value within a given range, it is best described as:

Accepted Answer

Continuous

Question 18

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter describes a population, while a statistic describes a sample.

Question 19

A variable $$X is $$measured for each individual in a population. The collection of all observed values of $$X is $$called:

Accepted Answer

Data

Question 20

Which of the following is a real-world example of a continuous variable?

Accepted Answer

Height of a mountain

Introduction to Statistics: Key Concepts and Foundations

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