Question 1

A statistic is typically a known quantity while a parameter is typically an unknown quantity.

Accepted Answer

This is a commonly accepted definition in statistics.

Question 2

Which of the following is a measure of the reliability of a statistical inference?
A)A population parameter.
B)A significance level.
C)A descriptive statistic.
D)A sample statistic.

Accepted Answer

A significance level (often denoted as alpha or α) is a measure used in hypothesis testing to determine the threshold at which the null hypothesis is rejected, thus it directly relates to the reliability of a statistical inference. Lower significance levels indicate higher reliability.

Question 3

The significance level measures the proportion of the time an inference about a population will be correct in the long run.

Accepted Answer

The significance level, typically denoted as alpha, represents the maximum probability of making a Type I error (rejecting a true null hypothesis) when testing a hypothesis. It does not directly measure the proportion of correct inferences in the long run, although it indirectly affects the balance between Type I and Type II errors and the overall accuracy of statistical tests. The probability of correctly rejecting a false null hypothesis, or the power of a test, depends on factors such as the sample size, effect size, and variability of the data.

Question 4

A summary measure that is computed from a population is called a:
A)sample.
B)statistic.
C)population.
D)parameter.

Accepted Answer

A parameter is a summary measure that is computed from a population, whereas a statistic is a summary measure that is computed from a sample. Therefore, option D is the correct answer.

Question 5

A councilman who is running for the office of senator of a state with 3.5 million registered voters commissions a survey. In the survey, 46% of the 8,000 registered voters interviewed say they plan to vote for him. The population of interest is:
A)the 3.5 million registered voters in the state.
B)the 8,000 registered voters interviewed.
C)the 46% who plan to vote for her.
D)all the residents of the state.

Accepted Answer

The population of interest in this survey is the entire group of registered voters in the state, which is 3.5 million. The survey was conducted with a sample of 8,000, which is intended to be representative of the larger population. Therefore, the survey results can be used to make inferences about the larger group of registered voters in the state. Options B and C are too narrow and do not represent the entire population of interest. Option D is too broad and includes individuals who may not be registered to vote.

Question 6

A company has developed a new engine whose average lifetime is unknown. In order to estimate this average, 100 engines are randomly selected from a large production line and tested; their average lifetime is found to be 11 years. The 11 years represents a:
A)parameter.
B)statistic.
C)sample.
D)population.

Accepted Answer

The average lifetime of the 100 engines is a statistic, as it is a numerical description of a sample (100 engines) taken from the larger population of engines produced by the company. A parameter would be the true average lifetime of all the engines produced by the company, which is unknown and being estimated through the sample.

Question 7

A resort employs 3,500 managers and staff. To ascertain their employees' opinions of a proposed health insurance plan, 350 employees are surveyed at random. The proportion of the 350 employees who favor the health insurance plan represents a parameter in this scenario.

Accepted Answer

The proportion of the 350 employees who favor the health insurance plan represents a statistic because it is a measure derived from a sample of the population, not the entire population itself.

Question 8

35% of a sample of 300 professional baseball players indicated that their parents did not play baseball. Based on this sample, we estimate that approximately 35% of the parents of all professional baseball players did not play baseball, plus or minus 5%. This is an example of using inferential statistics.

Accepted Answer

This statement is true. Inferential statistics is used to make inferences or predictions about a population based on a sample. In this case, the sample of 300 professional baseball players is used to estimate the proportion of all professional baseball players whose parents did not play baseball, with a margin of error of 5%.

Question 9

A random sample of 100 students is taken at LearnAll University and it's found that their average GPA is 3.1. If this information is used to help estimate the average GPA for all students at LearnAll University, which branch of statistics was applied?
A)Descriptive statistics
B)Inferential statistics
C)Sample statistics
D)Population statistics

Accepted Answer

Inferential statistics is used when we take a sample from a population and use that information to draw conclusions or make inferences about the population as a whole. In this case, the sample of 100 students was used to estimate the average GPA for all students at the university. Descriptive statistics, on the other hand, simply describe and summarize data from a sample or population. Sample statistics and population statistics refer to specific numerical measures, such as mean or standard deviation, calculated from a sample or population.

Question 10

A descriptive measure of a population is called a parameter.

Accepted Answer

A parameter refers to a descriptive measure of a population, while a statistic refers to a descriptive measure of a sample.

Question 11

A descriptive measure of a sample is called a parameter.

Accepted Answer

A parameter is a descriptive measure of a population, not a sample. A sample is typically described using statistics.

Question 12

A descriptive measure that is computed from a sample is called a:
A)parameter.
B)statistic.
C)population.
D)sample.

Accepted Answer

A descriptive measure computed from a sample is called a statistic. Parameters are descriptive measures computed from a population, while a population refers to the entire group being studied, and a sample is a subset of that population used for the study.

Question 13

A company has developed a new power cell and wants to estimate its average lifetime. A random sample of 650 power cells is tested and the average lifetime of this sample is found to be 315 hours. The 315 hours is the value of a:
A)parameter.
B)statistic.
C)sample.
D)population.

Accepted Answer

The value of 315 hours represents the average lifetime of the random sample of 650 power cells, and therefore it is a statistic. A parameter would be a value that represents the average lifetime of the entire population of power cells, which is unknown in this case. Sample and population are terms used to refer to the group of power cells being studied, rather than the specific value obtained from the sample.

Question 14

Statistical inference is the process of making an estimate, prediction, or decision about a population based on sample data.

Accepted Answer

This is the correct definition of statistical inference. It involves using sample data to draw conclusions about a larger population.

Question 15

A company has developed a new computer microprocessor whose average lifetime is unknown. In order to estimate this average, 300 microprocessors are randomly selected from a large production line and tested; their average lifetime is found to be 7 years. The 300 microprocessors represent a:
A)parameter.
B)statistic.
C)sample.
D)population.

Accepted Answer

The 300 microprocessors represent a sample, which is a subset of the larger population of microprocessors.

Question 16

A summary measure that is computed from a sample is called a statistic.

Accepted Answer

This is true. A statistic is a numerical value that describes a characteristic of a sample. Examples include the mean, standard deviation, and correlation coefficient calculated from the sample data.

Question 17

In a sample of 350 students selected from a large college of business, 25% are found to be marketing majors. The 25% is a statistic.

Accepted Answer

The statement is indicating a percentage which is a statistic, so it is true that the 25% is a statistic.

Question 18

You take a random sample to estimate a population mean and your results have a confidence level of 80%. That means the process you used will give you correct results 80% of the time.

Accepted Answer

The answer of You take a random sample to estimate...

Question 19

A population is the group of all items of interest to a statistics practitioner.

Accepted Answer

This is the definition of population in statistics.

Question 20

The confidence level is the proportion of times that an estimating procedure will be wrong in the long run.

Accepted Answer

The confidence level is actually the proportion of times that an estimating procedure will be correct in the long run. Therefore, the statement is false.

Quiz 1: What Is Statistics

A statistic is typically a known quantity while a parameter is typically an unknown quantity.

Which of the following is a measure of the reliability of a statistical inference?

The significance level measures the proportion of the time an inference about a population will be correct in the long run.

A summary measure that is computed from a population is called a:

A councilman who is running for the office of senator of a state with 3.5 million registered voters commissions a survey. In the survey, 46% of the 8,000 registered voters interviewed say they plan to vote for him. The population of interest is:

A company has developed a new engine whose average lifetime is unknown. In order to estimate this average, 100 engines are randomly selected from a large production line and tested; their average lifetime is found to be 11 years. The 11 years represents a:

A resort employs 3,500 managers and staff. To ascertain their employees' opinions of a proposed health insurance plan, 350 employees are surveyed at random. The proportion of the 350 employees who favor the health insurance plan represents a parameter in this scenario.

A random sample of 100 students is taken at LearnAll University and it's found that their average GPA is 3.1. If this information is used to help estimate the average GPA for all students at LearnAll University, which branch of statistics was applied?