Mathematical Statistics
| Description: Mathematical Statistics Quiz | |
| Number of Questions: 14 | |
| Created by: Aliensbrain Bot | |
| Tags: mathematical statistics probability hypothesis testing regression analysis time series analysis |
What is the probability of obtaining a head when flipping a fair coin?
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1/2
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1/3
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1/4
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1/5
Since a fair coin has two equally likely outcomes (head or tail), the probability of obtaining a head is 1/2.
In a hypothesis testing scenario, what is the null hypothesis?
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The hypothesis that is being tested
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The hypothesis that is assumed to be true
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The hypothesis that is rejected
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The hypothesis that is accepted
The null hypothesis is the statement that is assumed to be true until there is evidence to reject it.
What is the p-value in hypothesis testing?
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The probability of obtaining the observed data or more extreme data, assuming the null hypothesis is true
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The probability of rejecting the null hypothesis
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The probability of accepting the null hypothesis
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The probability of making a Type I error
The p-value is the probability of obtaining the observed data or more extreme data, assuming the null hypothesis is true.
What is the difference between Type I and Type II errors in hypothesis testing?
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Type I error is rejecting the null hypothesis when it is true, while Type II error is accepting the null hypothesis when it is false
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Type I error is accepting the null hypothesis when it is true, while Type II error is rejecting the null hypothesis when it is false
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Type I error is rejecting the null hypothesis when it is false, while Type II error is accepting the null hypothesis when it is true
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Type I error is accepting the null hypothesis when it is false, while Type II error is rejecting the null hypothesis when it is true
Type I error is rejecting the null hypothesis when it is true, while Type II error is accepting the null hypothesis when it is false.
What is the central limit theorem?
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The theorem that states that the sample mean of a large number of independent, identically distributed random variables will be approximately normally distributed
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The theorem that states that the sample variance of a large number of independent, identically distributed random variables will be approximately normally distributed
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The theorem that states that the sample median of a large number of independent, identically distributed random variables will be approximately normally distributed
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The theorem that states that the sample mode of a large number of independent, identically distributed random variables will be approximately normally distributed
The central limit theorem states that the sample mean of a large number of independent, identically distributed random variables will be approximately normally distributed.
What is the difference between a population and a sample?
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A population is the entire group of individuals or objects of interest, while a sample is a subset of the population
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A population is a subset of the entire group of individuals or objects of interest, while a sample is the entire group
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A population is the group of individuals or objects that are being studied, while a sample is the group of individuals or objects that are not being studied
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A population is the group of individuals or objects that are not being studied, while a sample is the group of individuals or objects that are being studied
A population is the entire group of individuals or objects of interest, while a sample is a subset of the population.
What is the difference between descriptive statistics and inferential statistics?
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Descriptive statistics are used to summarize and describe data, while inferential statistics are used to make inferences about a population based on a sample
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Descriptive statistics are used to make inferences about a population based on a sample, while inferential statistics are used to summarize and describe data
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Descriptive statistics are used to compare two or more groups of data, while inferential statistics are used to summarize and describe data
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Descriptive statistics are used to summarize and describe data, while inferential statistics are used to compare two or more groups of data
Descriptive statistics are used to summarize and describe data, while inferential statistics are used to make inferences about a population based on a sample.
What is the difference between a parameter and a statistic?
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A parameter is a numerical characteristic of a population, while a statistic is a numerical characteristic of a sample
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A parameter is a numerical characteristic of a sample, while a statistic is a numerical characteristic of a population
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A parameter is a qualitative characteristic of a population, while a statistic is a qualitative characteristic of a sample
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A parameter is a qualitative characteristic of a sample, while a statistic is a qualitative characteristic of a population
A parameter is a numerical characteristic of a population, while a statistic is a numerical characteristic of a sample.
What is the difference between a discrete random variable and a continuous random variable?
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A discrete random variable can take on only a finite or countable number of values, while a continuous random variable can take on any value within a specified range
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A discrete random variable can take on any value within a specified range, while a continuous random variable can take on only a finite or countable number of values
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A discrete random variable is a random variable that can take on only a finite number of values, while a continuous random variable is a random variable that can take on any value within a specified range
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A discrete random variable is a random variable that can take on any value within a specified range, while a continuous random variable is a random variable that can take on only a finite number of values
A discrete random variable can take on only a finite or countable number of values, while a continuous random variable can take on any value within a specified range.
What is the difference between a probability mass function and a probability density function?
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A probability mass function gives the probability of a discrete random variable taking on a specific value, while a probability density function gives the probability of a continuous random variable taking on a specific value
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A probability mass function gives the probability of a continuous random variable taking on a specific value, while a probability density function gives the probability of a discrete random variable taking on a specific value
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A probability mass function gives the probability of a random variable taking on a specific value, while a probability density function gives the probability of a random variable taking on any value within a specified range
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A probability mass function gives the probability of a random variable taking on any value within a specified range, while a probability density function gives the probability of a random variable taking on a specific value
A probability mass function gives the probability of a discrete random variable taking on a specific value, while a probability density function gives the probability of a continuous random variable taking on a specific value.
What is the difference between a cumulative distribution function and a probability density function?
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A cumulative distribution function gives the probability that a random variable will take on a value less than or equal to a specified value, while a probability density function gives the probability that a random variable will take on a specific value
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A cumulative distribution function gives the probability that a random variable will take on a specific value, while a probability density function gives the probability that a random variable will take on a value less than or equal to a specified value
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A cumulative distribution function gives the probability that a random variable will take on a value greater than or equal to a specified value, while a probability density function gives the probability that a random variable will take on a specific value
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A cumulative distribution function gives the probability that a random variable will take on a value greater than a specified value, while a probability density function gives the probability that a random variable will take on a specific value
A cumulative distribution function gives the probability that a random variable will take on a value less than or equal to a specified value, while a probability density function gives the probability that a random variable will take on a specific value.
What is the difference between a joint probability distribution and a marginal probability distribution?
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A joint probability distribution gives the probability of two or more random variables taking on specific values, while a marginal probability distribution gives the probability of a single random variable taking on a specific value
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A joint probability distribution gives the probability of a single random variable taking on a specific value, while a marginal probability distribution gives the probability of two or more random variables taking on specific values
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A joint probability distribution gives the probability of a random variable taking on a value less than or equal to a specified value, while a marginal probability distribution gives the probability of a random variable taking on a specific value
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A joint probability distribution gives the probability of a random variable taking on a specific value, while a marginal probability distribution gives the probability of a random variable taking on a value greater than or equal to a specified value
A joint probability distribution gives the probability of two or more random variables taking on specific values, while a marginal probability distribution gives the probability of a single random variable taking on a specific value.
What is the difference between a correlation and a regression?
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A correlation measures the strength and direction of the linear relationship between two variables, while a regression model predicts the value of one variable based on the value of another variable
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A correlation measures the strength and direction of the nonlinear relationship between two variables, while a regression model predicts the value of one variable based on the value of another variable
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A correlation measures the strength and direction of the relationship between two variables, while a regression model predicts the value of one variable based on the values of two or more other variables
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A correlation measures the strength and direction of the relationship between two variables, while a regression model predicts the values of two or more variables based on the value of another variable
A correlation measures the strength and direction of the linear relationship between two variables, while a regression model predicts the value of one variable based on the value of another variable.
What is the difference between a time series and a cross-sectional study?
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A time series study observes the same individuals or objects over time, while a cross-sectional study observes different individuals or objects at a single point in time
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A time series study observes different individuals or objects over time, while a cross-sectional study observes the same individuals or objects at a single point in time
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A time series study observes the same individuals or objects at a single point in time, while a cross-sectional study observes different individuals or objects over time
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A time series study observes different individuals or objects at a single point in time, while a cross-sectional study observes the same individuals or objects over time
A time series study observes the same individuals or objects over time, while a cross-sectional study observes different individuals or objects at a single point in time.