Stats Test 1

If r equals​_______, then a perfect negative linear relation exists between the two quantitative variables.

-1

The relative frequencies add up to _____.

1

Determine whether the following statement is true or false. Explain. Inferences based on voluntary response samples are generally not reliable. Choose the correct answer below. A.True, because it is often the case that the individuals who volunteer do not accurately represent the population. B.False, because a surveyor cannot force volunteers to respond. C.True, because the group that volunteers may not be a large enough sample size. D.​False, because individuals who volunteer are least likely to have personal bias.

A

Determine whether the following statement is true or false. Explain. When conducting a cluster​ sample, it is better to have fewer clusters with more individuals when the clusters are heterogeneous. Choose the correct answer below. A.True, because when the clusters are​ heterogeneous, they are scaled down versions of the population. B.False. It is better to have fewer clusters when the clusters are homogeneous. C.False, because the proportion of individuals per cluster to the population should not be affected by whether or not the clusters are heterogeneous. D.True, because heterogeneous clusters are not likely to resemble population​ heterogeneity, increasing the number of necessary individuals.

A

Explain the difference between a population and a sample. A. A population is the entire group that is being studied while a sample is a subset of the population that is being studied. B. A population is a person or object that is a member of the sample being studied while a sample is the entire group that is being studied. C. A population is the entire group that is being studied while a sample is a person or object that is a member of the population being studied. D. A population is a subset of the sample that is being studied while a sample is the entire group that is being studied.

A

If the linear correlation between two variables is​ negative, what can be said about the slope of the regression​ line? Choose the correct answer below. A.Negative B.Positive C.More information is needed

A

True or​ False: Chebyshev's inequality applies to all distributions regardless of​ shape, but the empirical rule holds only for distributions that are bell shaped. Choose the correct answer below. A.True, Chebyshev's inequality is less precise than the empirical​ rule, but will work for any​ distribution, while the empirical rule only works for​ bell-shaped distributions. B.False, both​ Chebyshev's inequality and the empirical rule will only work for​ bell-shaped distributions. C.​False, both​ Chebyshev's inequality and the empirical rule will work for any distribution. D.False, the empirical rule is less precise than​ Chebyshev's inequality, but will work for any​ distribution, while​ Chebyshev's inequality only works for​ bell-shaped distributions.

A

What does it mean to say that two variables are positively​ associated? A. There is a linear relationship between the​ variables, and whenever the value of one variable​ increases, the value of the other variable increases. B. There is a relationship between the variables that is not linear. C. There is a linear relationship between the variables. D. There is a linear relationship between the​ variables, and whenever the value of one variable​ increases, the value of the other variable decreases.

A

What is a bar​ graph? A. A bar graph is a horizontal or vertical representation of the frequency or relative frequency of the categories. The height of each rectangle represents the​ category's frequency or relative frequency. B.A bar graph represents the frequencies of values either from​ left-to-right or​ right-to-left. The different segments of the bar are used to indicate the different frequencies of each category. C.A bar graph is a circular graph that uses bars to divide it into segments corresponding to each category. The segments are proportional to the frequency of its category.

A

What is a confounding​ variable? A.A confounding variable is an explanatory variable that was considered in a study whose effect cannot be distinguished from a second explanatory variable in the study. B.A confounding variable is a response variable that has an effect on the explanatory​ variable, but it cannot be accurately measured in the study. C.A confounding variable is the explanatory variable on which a study has been focused. D. A confounding variable is a response variable that was not considered in a study whose effect cannot be distinguished from a second explanatory variable in the study.

A

What is a designed​ experiment? A. A designed experiment is when a researcher assigns individuals to a certain​ group, intentionally changing the value of an explanatory​ variable, and then recording the value of the response variable for each group. B. A designed experiment measures the value of the response variable without attempting to influence the value of either the response or explanatory variables. C. A designed experiment is a list of all individuals in a population along with certain characteristics of each individual.

A

What is a​ frame? Choose the correct answer below. A. A frame is a list of the individuals in the population being studied. B. A frame is the population being studied. C. A frame is the sample taken from the population being studied. D. A frame is a list of the individuals in the sample being studied.

A

What is meant by​ confounding? A.Confounding in a study occurs when the effects of two or more explanatory variables are not separated.​ Therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable or variables not accounted for in the study. B.Confounding in a study occurs when there is little or no actual relationship between the explanatory and response variable other than random chance. This sometimes causes completely unrelated variables to appear to have a causal​ relationship, and can cause variables that have almost no relationship to have a very strong relationship. C.Confounding in a study occurs when the effects of the explanatory variable are​ caused, in some​ part, by the effects of the response variable. When there is zero confounding in a​ study, the effects of the response variable are entirely caused by the effects of the explanatory variable. D.Confounding in a study occurs when a single explanatory variable has a great effect on a response variable. This sometimes causes a misleading interpretation of the relationship between the two variables.

A

Which sampling method does not require a​ frame? Choose the correct answer below. A.Systematic B.Simple random C.Stratified D.Cluster E.All of the above sampling methods require a frame

A

A ___________allows the researcher to claim causation between an explanatory variable and a response variable

A designed experiment

Determine whether the following statement is true or false. Explain. A simple random sample is always preferred because it obtains the same information as other sampling plans but requires a smaller sample size. Choose the correct answer below. A.True, because every individual has an equal chance of selection. B.False, because other sampling techniques may provide more information for less cost than a simple random sample. C.False, because simple random samples require a larger sample size than most other sampling methods. D.True, because it does not require extra preparation and can return more information than the other sampling techniques.

B

Is the statement below true or​ false? There is not one particular frequency distribution that is​ correct, but there are frequency distributions that are less desirable than others. Choose the correct answer below. A.The statement is true. Any correctly constructed frequency distribution is valid.​ However, some are less desirable because they take up more space. B.The statement is true. Any correctly constructed frequency distribution is valid.​ However, some choices for the categories or classes give more information about the shape of the distribution. C.The statement is false. All correctly constructed frequency distributions for a given data set are valid and give the same information. D.The statement is false. There is only one correct frequency distribution for any given data set.

B

What does it mean if a statistic is​ resistant? Choose the correct answer below. A.Changing particular data values affects its value substantially. B.Extreme values​ (very large or​ small) relative to the data do not affect its value substantially. C.An estimate of its value is extremely close to its actual value. D.Extreme values​ (very large or​ small) relative to the data affect its value substantially.

B

What does it mean when an observational study is​ retrospective? A.An retrospective study is a list of all individuals in a population along with certain characteristics of each individual. B.A retrospective study requires that individuals look back in time or require the researcher to look at existing records. C.A retrospective study collects the data over time.

B

What is a Pareto​ chart? A.A Pareto chart is a combination of a pie chart and a bar graph. B.A Pareto chart is a bar graph whose bars are drawn in decreasing order of frequency or relative frequency. C.A Pareto chart is a display of two data sets side by side where the height of each rectangle represents the​ category's frequency or relative frequency.

B

What is an observational​ study? A. An observational study is when a researcher assigns individuals to a certain​ group, intentionally changing the value of an explanatory​ variable, and then recording the value of the response variable for each group. B. An observational study measures the value of the response variable without attempting to influence the value of either the response or explanatory variables. C. An observational study is a list of all individuals in a population along with certain characteristics of each individual.

B

What is a​ cross-sectional study? Choose the correct answer below. A.Cross-sectional studies first identify a group of individuals to participate in the study. These individuals are then observed over a period of time. Over this period of​ time, characteristics about the individual are recorded. B.Cross-sectional studies are observational studies that collect information about individuals at a specific point in time or over a very short period of time. C.Cross-sectional studies are observational studies that are​ retrospective, meaning that they require individuals to look back in time or require the researcher to look at existing records. D.Cross-sectional studies are a list of all individuals in a population along with certain characteristics of each individual.

B

What is the difference between univariate data and bivariate​ data? Choose the correct answer below. A.In univariate​ data, there is one mean. In bivariate​ data, there are two means. B.In univariate​ data, a single variable is measured on each individual. In bivariate​ data, two variables are measured on each individual. C.In univariate​ data, there are only positive values and zeros. In bivariate​ data, there are positive​ values, negative​ values, and zeros. D.In univariate​ data, the data are qualitative. In bivariate​ data, the data are quantitative.

B

For heights of full dash grown men​, state whether you would expect a histogram of the data to be​ bell-shaped, uniform, skewed​ left, or skewed right. Choose the correct answer below. Bell shaped Skewed right Uniform Skewed left

Bell shaped

For scores on a standardized exam such as the SAT​, state whether you would expect a histogram of the data to be​ bell-shaped, uniform, skewed​ left, or skewed right. Choose the correct answer below. Bell shaped Skewed right Uniform Skewed left

Bell shaped

A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be​ larger, the mean or the​ median? Why? Choose the correct answer below. A.The median will likely be larger because the extreme values in the right tail tend to pull the median in the direction of the tail. B.The median will likely be larger because the extreme values in the left tail tend to pull the median in the opposite direction of the tail. C.The mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail. D.The mean will likely be larger because the extreme values in the left tail tend to pull the mean in the opposite direction of the tail.

C

Determine whether the following statement is true or false. Explain. When obtaining a stratified​ sample, the number of individuals included within each stratum must be equal. Choose the correct answer below. A.True. Sampling the same number of people from each stratum will result in a sample that is representative of the population at a lower cost than a simple random sample. B.False. A stratified sample is constructed by successively selecting a stratum at random and then selecting a random individual from within that stratum. With this​ process, it is unlikely that all strata will be sampled from the same number of times. C.False. Within stratified​ samples, the number of individuals sampled from each stratum should be proportional to the size of the strata in the population. D.False. When taking a stratified​ sample, a simple random sample is drawn from one stratum at random. All other strata will not be included in the sample.

C

The U.S. Department of Housing and Urban Development​ (HUD) uses the median to report the average price of a home in the United States. Why do you think HUD uses the​ median? A.HUD uses the median because the data are bimodal. B.HUD uses the median because the data are skewed left. C.HUD uses the median because the data are skewed right. D.HUD uses the median because the data are symmetrical.

C

What does it mean to say that two variables are negatively​ associated? A.There is a linear relationship between the variables. B.There is a linear relationship between the​ variables, and whenever the value of one variable​ increases, the value of the other variable increases. C.There is a linear relationship between the​ variables, and whenever the value of one variable​ increases, the value of the other variable decreases. D.There is a relationship between the variables that is not linear.

C

What does it mean when an observational study is​ prospective? A.A prospective study requires that individuals look back in time or require the researcher to look at existing records. B.An prospective study is a list of all individuals in a population along with certain characteristics of each individual. C.A prospective study collects the data over time.

C

What is a lurking​ variable? A.A lurking variable is a response variable that was not considered in a​ study, but is also affected by the casual relationship of the explanatory variables in the study. In​ addition, lurking variables are typically related to response variables in the study. B.A lurking variable is a quantitative variable that has an infinite number of possible values that are not countable. In​ addition, lurking variables are typically very large numbers that make them​ difficult, if not​ impossible, to include in a study. C.A lurking variable is an explanatory variable that was not considered in a​ study, but that affects the value of the response variable in the study. In​ addition, lurking variables are typically related to explanatory variables in the study. D.A lurking variable is a quantitative variable that has either a finite number of possible values or a countable number of possible values. In​ addition, lurking variables are typically equal to​ zero, or almost equal to zero.

C

______are the categories by which data are grouped.

Classes

Define simple random sampling. Choose the correct answer below. A.Simple random sampling is the process of obtaining a sample of size n from a population of the same size n. The sample is then called a simple random sample. B.Simple random sampling is the process of using chance to select individuals from a population to be included in the sample. The sample is then called a simple random sample. C.Simple random sampling is the process of selecting individuals from a population using a convenient sample. The sample is then called a simple random sample. D.A sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring. The sample is then called a simple random sample.

D

Define statistics. A.Statistics is the science of​ manipulating, reorganizing, and editing information to produce the desired results. In​ addition, statistics is about providing the required answer with the desired level of confidence. B.Statistics encompasses all scientific disciplines in which random occurrences are analyzed. In​ addition, statistics references any random occurrence which is reported using percentages or proportions. C.Statistics encompasses all scientific disciplines in which percentages are​ used, data are​ analyzed, and probabilities are found. In​ addition, statistics references any mathematical model which is reported using percentages or proportions. D.Statistics is the science of​ collecting, organizing,​ summarizing, and analyzing information to draw a conclusion and answer questions. In​ addition, statistics is about providing a measure of confidence in any conclusions.

D

True or​ False: When comparing two​ populations, the larger the standard​ deviation, the more dispersion the distribution​ has, provided that the variable of interest from the two populations has the same unit of measure. Choose the correct answer below. A.True, because the standard deviation is the difference between the largest and smallest observation. When the standard deviation is​ larger, there is more distance between the largest and smallest​ observation, and​ therefore, more dispersion in the distribution. B.False, because the larger the standard deviation​ is, the less dispersion the distribution has. C.False, because the standard deviation measures the spread of the​ distribution, not the dispersion of the distribution. D.​True, because the standard deviation describes how​ far, on​ average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical​ value, and​ therefore, more dispersed.

D

What does it mean when sampling is done without​ replacement? Choose the correct answer below. A.Once a sample is​ taken, those individuals are no longer considered part of the population. B.Once a sample is​ taken, those individuals cannot be selected for any other samples. C.Once an individual is​ selected, the individual can be selected again. D.Once an individual is​ selected, the individual cannot be selected again.

D

Why​ shouldn't classes overlap when summarizing continuous data in a frequency or relative frequency​ distribution? Choose the correct answer below. A.Classes​ shouldn't overlap so that they are open ended. B.Classes​ shouldn't overlap so that the class width is as small as possible. C.Classes​ shouldn't overlap so that the distribution is not skewed in one direction. D.Classes​ shouldn't overlap so there is no confusion as to which class an observation belongs.

D

_____________ statistics consists of organizing and summarizing information​ collected, while _____________ statistics uses methods that generalize results obtained from a sample to the population and measure the reliability of the results.

Descriptive statistics consists of organizing and summarizing information​ collected, while inferential statistics uses methods that generalize results obtained from a sample to the population and measure the reliability of the results.

True or​ False: A data set will always have exactly one mode.

False

True or​ false: Correlation implies causation.

False

_______ divide data sets in fourths.

Quartiles

Determine whether each variable is​ qualitative, continuous, or discrete. Size is a ____________variable. Screen type is a __________ variable. Number of channels available is a _______variable.

Size is a continuous variable. Screen type is a qualitative variable. Number of channels available is a discrete variable.

For ages of hearing dash aid patients​, state whether you would expect a histogram of the data to be​ bell-shaped, uniform, skewed​ left, or skewed right. Choose the correct answer below. Bell shaped Skewed right Uniform Skewed left

Skewed left

For annual household incomes in a country​, state whether you would expect a histogram of the data to be​ bell-shaped, uniform, skewed​ left, or skewed right. Choose the correct answer below. Bell shaped Skewed right Uniform Skewed left

Skewed right

The standard deviation is used in conjunction with the​ ______ to numerically describe distributions that are bell shaped. The​ ______ measures the center of the​ distribution, while the standard deviation measures the​ ______ of the distribution.

The standard deviation is used in conjunction with the​ __mean____ to numerically describe distributions that are bell shaped. The​ __mean____ measures the center of the​ distribution, while the standard deviation measures the​ ___spread___ of the distribution.

Is the statement below true or​ false? The​ least-squares regression line always travels through the point (x̄,ȳ).

True

For ages of students in a public school​, state whether you would expect a histogram of the data to be​ bell-shaped, uniform, skewed​ left, or skewed right. Choose the correct answer below. Bell shaped Skewed right Uniform Skewed left

Uniform

_________ are the characteristics of the individuals of the population being studied.

Variables

The​ _________________ is the difference between consecutive lower class limits.

class width

​A(n) ________________is obtained by dividing the population into groups and selecting all individuals from within a random sample of the groups.

cluster sample

​A(n) _________ is a person or object that is a member of the population being studied.

individual

The​ ______ class limit is the smallest value within the class and the​ ______ class limit is the largest value within the class.

lower; upper

A frequency distribution lists the _____ of occurrences of each category of​ data, while a relative frequency distribution lists the _____ of occurrences of each category of data.

number; proportion

​A(n) _________ is a numerical summary of a population.

parameter

μ

population mean

σ

population standard deviation

σ^2

population variance

In a​ boxplot, if the median is to the left of the center of the box and the right whisker is substantially longer than the left​ whisker, the distribution is skewed _____

right

x̄

sample mean

s

sample stand deviation

s^2

sample variance

For a number of children in a family​, state whether you would expect a histogram of the data to be​ bell-shaped, uniform, skewed​ left, or skewed right. Choose the correct answer below. Bell shaped Skewed right Uniform Skewed left

skewed right

For a number of people living in a household​, state whether you would expect a histogram of the data to be​ bell-shaped, uniform, skewed​ left, or skewed right. Choose the correct answer below. Bell shaped Skewed right Uniform Skewed left

skewed right

For car prices​, state whether you would expect a histogram of the data to be​ bell-shaped, uniform, skewed​ left, or skewed right. Choose the correct answer below. Bell shaped Skewed right Uniform Skewed left

skewed right

​A(n)_________ is a numerical summary of a sample.

statistic

​A(n) ________________ is obtained by dividing the population into homogeneous groups and randomly selecting individuals from each group.

stratified sample

The​ _______ represents the number of standard deviations an observation is from the mean.

z-score

The sum of the deviations about the mean always equals _____

zero