Question 1

You randomly select someone from a group of 12. Two of those in the group were born in Iowa. What is the chance you will pick a person born in Iowa?

Accepted Answer

The chance of picking a person born in Iowa is equal to the number of people born in Iowa divided by the total number of people in the group. Since there are two people born in Iowa and 12 total people in the group, the chance is 2/12 or approximately 0.17. Therefore, the best choice is B.

Question 2

The fact that probabilities are proportions means that they:

Accepted Answer

Probabilities are ratios of the number of desired outcomes to the total number of outcomes. Therefore, the probabilities can't be lower than zero (when there are no desired outcomes) or more than one (when all the outcomes are desired).

Question 3

In a housing project there are 350 households in which English is usually spoken, 50 in which Spanish is usually spoken, and 100 in which the language is other than English or Spanish. A researcher approaches a house at random to conduct an interview. What is the chance that the usual language in that household will NOT be English?

Accepted Answer

The total number of households is 500 (350 English-speaking + 50 Spanish-speaking + 100 other languages). The number of households in which English is not spoken is 150 (50 Spanish-speaking + 100 other languages). Therefore, the probability that a randomly selected household does not speak English as the usual language is 150/500, which simplifies to 0.3 or 30%.

Question 4

You wish to survey the interests of students in your statistics class. You enter the names of all students onto an Excel spreadsheet. You then use a computer program to generate a list of random names. This is called:

Accepted Answer

The method described is random selection, which is the best choice for obtaining an unbiased sample of the population. Computerized selection, haphazard selection, and sampling selection may introduce bias into the sample selection process.

Question 5

A researcher conducts extensive interviews with 40 workers at a large factory in order to examine the morale among workers in general at that factory. In this example, what is the population?

Accepted Answer

The population in this example is all the workers in the factory, not just the 40 that were interviewed. This is because the researcher is trying to make generalizations about the morale among workers in general at that factory, so they need to have information about all the workers in order to draw accurate conclusions. Option A is incorrect because the 40 workers interviewed are only a sample of the larger population. Option B is incorrect because it excludes the 40 workers interviewed, which are still part of the overall population. Option D is incorrect because it extends beyond the scope of the study, which is focused on the workers at one specific factory, not all factory workers in the United States.

Question 6

Survey organizations in the United States today are not allowed to call ____________ , creating some bias in the poll results.

Accepted Answer

Survey organizations are not allowed to call cell phones due to regulations set by the Federal Communications Commission (FCC). This creates bias in the poll results because certain demographics, such as young adults and low-income individuals, are more likely to rely solely on cell phones and may not be represented in the survey.

Question 7

You have an aquarium full of tropical salt-water fish and you need to know the exact salt content of the water. To test it, you take a cup and scoop some of the water out. In statistical language, the scoop of water is a:

Accepted Answer

The scoop of water represents a subset of the entire population of water in the aquarium, so it is a sample. Since you are measuring the salt content of the scoop of water, you are obtaining a statistic, not a parameter. A population distribution would refer to the distribution of the entire population of salt water in the aquarium, which is not relevant in this scenario.

Question 8

The Gallup Poll correctly predicted George H. W. Bush's 1988 victory using only 4,089 interviews. Why, then, did the Gallup Poll in 1948 wrongly predict Dewey's victory over Truman when they used 50,000 interviews to make the prediction?

Accepted Answer

In 1948, the Gallup Poll used quota sampling, which is prone to selection bias and can result in an unrepresentative sample. In contrast, in 1988, the poll used random sampling, which is more representative of the population and produces more accurate predictions.

Question 9

Relative frequency is:

Accepted Answer

Relative frequency is the number of times something occurs relative to the number of times it could have occurred. It is expressed as a proportion or percentage. It is a measure of how frequently a result occurs, but not the expected number of times or the outcome of repeating an experiment.

Question 10

In figuring probabilities, expected relative frequency is:

Accepted Answer

Expected relative frequency is the number of successful outcomes divided by the number of total outcomes expected if you repeat an experiment a large number of times. It is a measure of the likelihood of a particular outcome occurring based on the number of times the experiment is repeated.

Question 11

You want to study the general amount of drug use at your university. You obtain a complete list of students. You then put all the names into a box and have a blindfolded person select as many people as you needed. This is called:

Accepted Answer

Random selection ensures that each individual in the population has an equal and independent chance of being selected for the study, which helps to reduce the potential for bias and increase the representativeness of the sample. Haphazard selection (B) relies on the researcher's personal judgment and may not be truly random, while specified selection (C) and type B selection (D) are not recognized methods of sampling in research.

Question 12

Since 1948, all survey organizations have used the "probability method" to increase the accuracy of their results. What type of sampling method is utilized as part of this new method?

Accepted Answer

The "probability method" involves the use of random sampling techniques, and multistage cluster sampling is a common type of random sampling that is used to increase the accuracy of survey results. Unitary cluster sampling and quota sampling are other types of sampling methods, but they are less commonly used in the probability method. Inferential sampling may refer to the process of making inferences about a population based on a sample, but it is not a specific type of sampling method.

Question 13

To change a proportion into a percent:

Accepted Answer

To change a proportion into a percent, we need to multiply it by 100 to move the decimal point two places to the right.

Question 14

If you were to select a score at random from a distribution that follows a normal curve, what approximately is the probability of selecting a score between Z scores of 0 and +1?

Accepted Answer

The area under a normal curve between Z scores of 0 and +1 is approximately 34%. This is a well-known fact in statistics and can be found by looking at a standard normal distribution table or using a calculator with a normal distribution function. Therefore, the correct answer is C, which corresponds to the 34% probability.

Question 15

You want to study the physical effects of caffeine. To recruit participants for your experiment you post a sign-up sheet for anyone willing to participate. This is an example of:

Accepted Answer

Haphazard selection refers to a non-systematic approach to choosing participants, such as posting a sign-up sheet and allowing anyone interested to participate. This method does not ensure a representative sample and is based on convenience rather than random or strategic criteria.

Question 16

In statistics writing, it is common to use Greek letters for:

Accepted Answer

Greek letters are often used to represent population parameters in statistics writing. Populations are typically denoted with Greek letters, while sample statistics are denoted with Roman letters.

Question 17

If you want to know something about a population, your results would be MOST accurate if you could study the:

Accepted Answer

Studying the entire population would give the most accurate results as it would eliminate any selection bias or the possibility of a non-representative sample. However, this can be impractical or impossible in many cases, so sampling a representative subset of the population is often used as a compromise.

Question 18

Whenever possible, researchers report the proportion of individuals approached for a study who actually participated. This is called:

Accepted Answer

The proportion of individuals who actually participated in a study out of all those who were approached is called the response rate. Option A, attrition rate, refers to the proportion of participants who drop out of a study over time. Option B, random selection rate, is not a common term used in research. Option C, approach rate, refers to the proportion of individuals who agreed to participate after being contacted, but it does not take into account those who were not reached or refused to participate.

Question 19

In a single throw of a die, what is the probability of attaining a number of 4 or lower?

Accepted Answer

There are 4 possible outcomes out of 6 that are 4 or lower (1, 2, 3, and 4), so the probability of attaining a number of 4 or lower is 4/6 or 2/3, which is approximately 0.67. Therefore, the best choice is B.

Question 20

The actual values of the mean, variance, and standard deviation of a population are called:

Accepted Answer

Mean, variance, and standard deviation are all measures of central tendency and variability that describe a population. Thus, they are population parameters. Sample statistics, on the other hand, are estimates of population parameters that are calculated using data from a sample of the population. Population Z scores and regressed standardized scores are not relevant to this concept.

Quiz 4: Some Key Ingredients for Inferential Statistics: the Normal Curve, Sample Versus Population, and Probability