Question 1

The null and alternative hypotheses ______.
A) are mutually exclusive from each other
B) contain values of a sample statistic such as the sample mean (  )
C) are two types of research hypotheses
D) state the critical values of a statistic needed to reject the null hypothesis

Accepted Answer

The answer of The null and alternative hypotheses ______.
A) are...

Question 2

In which of the following steps of analyzing data is probability most important?
A) calculating measures of central tendency such as the mean or median
B) developing research hypotheses
C) examining your data by creating tables and figures
D) calculating inferential statistics

Accepted Answer

Probability is most important in calculating inferential statistics, as these methods involve using probability theory to make inferences about a population based on a sample of data.

Question 3

A researcher finds that the mean income for her sample is $40,500 but the mean for the population from which the sample is drawn is believed to be $44,270. The difference between the two means can be attributed to ______.
A) nonrandom sampling
B) normal sampling
C) luck
D) sampling error

Accepted Answer

The difference between the sample mean and population mean can be attributed to sampling error, which is the natural variation that occurs between samples and the population.

Question 4

The sum of the probabilities for the values of a binomial variable equals ______.
A) 1.00
B) .50
C) 2.00
D) zero

Accepted Answer

The sum of the probabilities for all possible outcomes of a binomial variable must equal 1.00, as these outcomes represent all possible events that can occur.

Question 5

A ______ is a statement about an expected outcome or relationship involving population parameters.
A) null hypothesis
B) statistical hypothesis
C) sampling error
D) alternative hypothesis

Accepted Answer

A statistical hypothesis is a statement about the expected outcome or relationship between population parameters. The null hypothesis (A) is a specific type of statistical hypothesis that assumes there is no relationship between variables or no difference between groups. Sampling error (C) refers to the natural variation that occurs when taking a sample from a population. The alternative hypothesis (D) is a competing hypothesis to the null hypothesis and assumes that there is a relationship between variables or a difference between groups.

Question 6

Sampling error refers to differences between ______.
A) statistics calculated from a sample and statistics pertaining to the population from which the sample is drawn
B) statistics calculated from two different populations
C) the likelihood of an occurrence of a particular outcome of an event and all possible outcomes
D) the likelihood of being in one category versus another category

Accepted Answer

Sampling error refers to the differences between statistics calculated from a sample and statistics pertaining to the population from which the sample is drawn. It is a measure of the extent to which sample statistics differ from population parameters.

Question 7

Which of the following is the last step in the process of hypothesis testing?
A) make a decision regarding the null hypothesis
B) calculate the appropriate statistic
C) relate the result of the analysis to the research hypothesis
D) state the null and alternative hypothesis

Accepted Answer

The last step in the process of hypothesis testing involves relating the result of the analysis to the research hypothesis to interpret the findings in the context of the research question being investigated.

Question 8

In which of the following steps of the research process is probability most important?
A) developing a research hypothesis
B) collecting data
C) calculating descriptive statistics
D) calculating inferential statistics

Accepted Answer

Probability is most important in calculating inferential statistics, which allow researchers to make conclusions and generalizations about a population based on a sample of data. Inferential statistics use probability to determine the likelihood that the findings from the sample are representative of the population as a whole.

Question 9

A researcher finds that the mean number of arrests for juveniles in his sample is .39 whereas the mean number of arrests in the population is .15 The difference between the two means can be attributed to ______.
A) non-normal error
B) luck
C) a lack of planning
D) sampling error

Accepted Answer

The difference between the sample mean and the population mean can be attributed to sampling error, which is a natural result of selecting a sample from a population. It is likely that the researcher's sample was not a perfect representation of the population, leading to the difference in mean number of arrests. Non-normal error, luck, and a lack of planning are less likely explanations for the difference.

Question 10

Which of the following is an example of a binomial variable?
A) length of sentence
B) race (White or non-White)
C) age (in years)
D) education (<high school, high school diploma, some college, college degree)

Accepted Answer

A binomial variable is one that has two and only two outcomes. In this case, race categorized as White or non-White fits the criteria, making it a binomial variable.

Question 11

Which of the following is the correct order for the steps in hypothesis testing?
A) State the null and alternative hypotheses; make a decision about the null hypothesis; draw a conclusion; relate the results to the research hypothesis.
B) State the null and alternative hypotheses; make a decision about the null hypothesis; relate the results to the research hypothesis; draw a conclusion.
C) State the null and alternative hypotheses; draw a conclusion; make a decision about the null hypothesis; relate the results to the research hypothesis.
D) State the null and alternative hypotheses; draw a conclusion; relate the results to the research hypothesis; make a decision about the null hypothesis.

Accepted Answer

The correct order for hypothesis testing starts with stating the null and alternative hypotheses, followed by making a decision about the null hypothesis (based on statistical analysis), then drawing a conclusion, and finally relating the results back to the research hypothesis.

Question 12

Probability is an important concept for researchers primarily because ______.
A) it helps researchers prove their hypotheses
B) researchers collect data from samples rather than populations
C) researchers test hypotheses about samples by collecting data from populations
D) most research involves flipping coins and pulling aces out of a deck of cards

Accepted Answer

Probability allows researchers to make inferences about populations based on sample data, since it's often impractical or impossible to collect data from entire populations.

Question 13

A researcher finds that the mean number of children in her sample is 3.48; however, the mean number of children in the population is 2.44. The difference between the two means can be attributed to ______.
A) systematic error
B) faulty logic
C) sampling error
D) non-random error

Accepted Answer

The difference between the sample mean and the population mean can be attributed to sampling error, which occurs due to the natural variations among different samples drawn from the same population.

Question 14

A binomial distribution is used for a variable ______.
A) consisting of exactly two categories
B) consisting of only one category
C) consisting of three categories
D) that has zero categories

Accepted Answer

A binomial distribution is used for a variable consisting of exactly two categories, often described as success or failure, where the probability of success is constant across each trial. It follows a specific set of rules and formulas, such as the binomial probability formula, which calculates the probability of a specific number of successes in a given number of trials.

Question 15

In which of the following steps of the research process is probability most important?
A) testing research hypotheses
B) examining one's data
C) developing research hypotheses
D) reviewing the existing literature on the topic of interest

Accepted Answer

Probability is most important in testing research hypotheses, as it provides a way to determine whether the results obtained are significant or simply due to chance. Probability calculations are used to determine the likelihood that the observed results occurred by chance, and to set criteria for rejecting or accepting a research hypothesis.

Question 16

If you were to draw 15 random samples of 100 residents in a city you may get 15 different means. These differences across samples may be defined as ______.
A) probability
B) random error
C) sampling error
D) normal error

Accepted Answer

Sampling error refers to the differences between the sample statistics (such as the mean) and the corresponding population parameters (such as the true population mean) that occur by chance due to random sampling variability. Therefore, the differences in means across the 15 random samples can be attributed to sampling error.

Question 17

Which of the following is the first step in hypothesis testing?
A) make a decision regarding the null hypothesis
B) calculate the appropriate statistic
C) relate the result of the analysis to the research hypothesis
D) state the null and alternative hypothesis

Accepted Answer

The first step in hypothesis testing is to state the null and alternative hypothesis.

Question 18

Which of the following variables would NOT be used for a binomial distribution?
A) age (over 65 or under 65)
B) gender (male or female)
C) jury verdict (guilty or not guilty
D) religion (Catholic, Protestant, Buddhist, etc.).

Accepted Answer

A binomial distribution requires only two possible outcomes or categories. Age, gender, and jury verdict all have only two possible outcomes and could be used in a binomial distribution. However, religion has more than two possible categories, so it would not be appropriate for a binomial distribution.

Question 19

Which of the following is an example of a binomial variable?
A) religion (Christian, Buddhist, Catholic, Agnostic)
B) race (White, Asian, African American, Hispanic, Native American)
C) age (over 65 or under 65)
D) highest degree (high school diploma, some college, BA, professional degree)

Accepted Answer

A binomial variable is a type of discrete variable that has only two possible outcomes (success or failure) and a fixed number of trials. In this case, age can be categorized as either over 65 or under 65, making it a binomial variable. The other options (religion, race, highest degree) do not have only two possible outcomes.

Question 20

Which of the following steps in the hypothesis testing process involves mathematical calculations?
A) state the null and alternative hypothesis
B) calculate the appropriate statistic
C) make a decision regarding the null hypothesis
D) draw a conclusion from the analysis

Accepted Answer

Calculating the appropriate statistic is a crucial step in hypothesis testing and involves mathematical calculations. The other steps in the process (such as stating the null and alternative hypothesis, making a decision regarding the null hypothesis, and drawing a conclusion from the analysis) involve decisions and judgments based on the results of the calculation.

Quiz 6: Probability and Hypothesis Testing

The null and alternative hypotheses ______.

In which of the following steps of analyzing data is probability most important?

A researcher finds that the mean income for her sample is $40,500 but the mean for the population from which the sample is drawn is believed to be $44,270. The difference between the two means can be attributed to ______.

The sum of the probabilities for the values of a binomial variable equals ______.

A ______ is a statement about an expected outcome or relationship involving population parameters.

Sampling error refers to differences between ______.

Which of the following is the last step in the process of hypothesis testing?

In which of the following steps of the research process is probability most important?

A researcher finds that the mean number of arrests for juveniles in his sample is .39 whereas the mean number of arrests in the population is .15 The difference between the two means can be attributed to ______.

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

Which of the following is the correct order for the steps in hypothesis testing?

Probability is an important concept for researchers primarily because ______.

A researcher finds that the mean number of children in her sample is 3.48; however, the mean number of children in the population is 2.44. The difference between the two means can be attributed to ______.

A binomial distribution is used for a variable ______.

In which of the following steps of the research process is probability most important?

If you were to draw 15 random samples of 100 residents in a city you may get 15 different means. These differences across samples may be defined as ______.

Which of the following is the first step in hypothesis testing?

Which of the following variables would NOT be used for a binomial distribution?

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

Which of the following steps in the hypothesis testing process involves mathematical calculations?