Podcast
Questions and Answers
Which of the following is NOT a primary concern when a major portion of statistics is focused on statistical inference?
Which of the following is NOT a primary concern when a major portion of statistics is focused on statistical inference?
- Testing a hypothesis.
- Calculating the exact population size. (correct)
- Making predictions based on sample data.
- Estimating a population parameter.
A population parameter's value is always known when conducting statistical analysis.
A population parameter's value is always known when conducting statistical analysis.
False (B)
What term describes a subset of the population that is used to make inferences about the entire population?
What term describes a subset of the population that is used to make inferences about the entire population?
Sample
The credibility of statistical inference heavily depends on the ______ of the sample used.
The credibility of statistical inference heavily depends on the ______ of the sample used.
Match the following terms with their definitions:
Match the following terms with their definitions:
What kind of variable is described by the population mean?
What kind of variable is described by the population mean?
The sample mean is also called a population mean estimator.
The sample mean is also called a population mean estimator.
A random variable whose value depends on the sample is known as what?
A random variable whose value depends on the sample is known as what?
A particular value of an estimator is referred to as an ______.
A particular value of an estimator is referred to as an ______.
Match each statistical term with its correct description:
Match each statistical term with its correct description:
What does the sampling distribution of the sample mean represent?
What does the sampling distribution of the sample mean represent?
Each sample can yield only one sample mean.
Each sample can yield only one sample mean.
If the expected value of an estimator equals the population parameter, the estimator is said to be what?
If the expected value of an estimator equals the population parameter, the estimator is said to be what?
The standard deviation of the sampling distribution of the sample mean is called the ______.
The standard deviation of the sampling distribution of the sample mean is called the ______.
Match the following concepts related to sampling distributions:
Match the following concepts related to sampling distributions:
According to the central limit theorem, what distribution does the sum or average of a large number of independent observations from the same distribution approximate?
According to the central limit theorem, what distribution does the sum or average of a large number of independent observations from the same distribution approximate?
The approximation by the normal distribution gets worse as the number of observations increases, according to the Central Limit Theorem.
The approximation by the normal distribution gets worse as the number of observations increases, according to the Central Limit Theorem.
What term describes the probability distribution of a sample proportion?
What term describes the probability distribution of a sample proportion?
According to the Central Limit Theorem, the sampling distribution is approximately ________ under certain conditions.
According to the Central Limit Theorem, the sampling distribution is approximately ________ under certain conditions.
Match the term with its correct statistical symbol or formula used in sampling and distributions:
Match the term with its correct statistical symbol or formula used in sampling and distributions:
Flashcards
Sample
Sample
A subset of the population used to make inferences about the population parameter.
Population Parameter
Population Parameter
A constant value, often unknown, that describes a characteristic of an entire population.
Statistic
Statistic
A random variable whose value depends on the chosen sample from a population.
Estimator (Point Estimator)
Estimator (Point Estimator)
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Estimate
Estimate
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Sampling Distribution of the Sample Mean
Sampling Distribution of the Sample Mean
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Standard Error
Standard Error
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Central Limit Theorem (CLT)
Central Limit Theorem (CLT)
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Binomial Distribution
Binomial Distribution
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Sampling Distribution of the Sample Proportion
Sampling Distribution of the Sample Proportion
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Study Notes
- Statistics are concerned with statistical inference.
Sampling
- Estimate a population parameter.
- Test a hypothesis.
Population
- Refers to all items of interest in a statistical problem.
- If there is access to the entire population (census), the parameters are known.
- Inference is thus not needed.
Sample
- Refers to a subset of the population.
- Sample statistics are used to make inferences about the unknown population parameter.
- The credibility of statistical inference depends on the sample's quality.
- The sample or survey should represent the population.
Population Parameter
- A constant with an unknown value.
- Describes a characteristic of the population.
- The population mean describes a quantitative variable.
- Population proportion describes a qualitative variable.
- It is important there is only one population.
- Many possible samples of a given size are drawn from it.
Statistic
- Refers to a random variable whose value depends on the sample.
- Describes a characteristic of a sample (one of many possible samples).
- Includes sample mean and sample proportion.
- Estimator/point estimator defines a statistic used to estimate a parameter.
- Estimate: indicates a particular value of the estimator.
- It's a random variable whose value depends on the chosen sample.
- Estimator of the population mean.
- The value of is an estimate.
Sampling Distribution of the Sample Mean
- The probability distribution derived from all the means that come from all possible samples of a given size.
- Consider a sample mean derived from n observations.
- Another sample mean is derived from a different sample of n observations.
- Repeat the process a large number of times.
- The frequency distribution of the sample means is the sampling distribution.
- Let X represent a certain characteristic of a population.
- Population mean
- Let the sample mean be based on a random sample of n observations.
Expected Value
- The expected value of is the same as the expected value of X.
- The average of the sample means is the average of the population.
- Unbiased refers to when the expected value of an estimator equals the population parameter.
Variance
- The variance of is less than
- This is because each sample will contain both high and low values that cancel on another.
- Standard error is the standard deviation
Central Limit Theorem
- The sum or average of a large number of independent observations from the same underlying distribution has an approximate normal distribution.
- Approximation improves as the number of observations increases.
- Practitioners use the normal distribution approximation when
- If is approximately, then any value can be transformed to a corresponding value.
Sample Proportion
-
A binomial distribution describes the number of successes X in n trials of a Bernoulli process where is the probability of success.
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Use the sample proportion P so the sample proportion is unbiased.
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The sampling distribution is approximately normal.
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When the proportion deviates from p=0.50, a larger sample size is needed for the approximation.
-
The approximation is justified when transformed into its corresponding z value.
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