Statistics: a Process of Making Inferences - Statistics
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What is a statistic in the context of inference?
What is a statistic in the context of inference?
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A numerical characteristic computed from a sample (random variable). Varies between samples due to sampling variability.
A numerical characteristic computed from a sample (random variable). Varies between samples due to sampling variability.
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What is a population parameter?
What is a population parameter?
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A numerical characteristic of a population (fixed, usually unknown). True value we estimate using sample statistics.
A numerical characteristic of a population (fixed, usually unknown). True value we estimate using sample statistics.
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Which inference goal matches $\bar{x}$: estimating a population mean or a population proportion?
Which inference goal matches $\bar{x}$: estimating a population mean or a population proportion?
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Estimating a population mean $\mu$. $\bar{x}$ is the sample mean, used to estimate population mean $\mu$.
Estimating a population mean $\mu$. $\bar{x}$ is the sample mean, used to estimate population mean $\mu$.
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Which sampling method best supports inference to a population: convenience sample or random sample?
Which sampling method best supports inference to a population: convenience sample or random sample?
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Random sample. Only random samples allow valid statistical inference.
Random sample. Only random samples allow valid statistical inference.
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What is sampling variability?
What is sampling variability?
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Natural variation in a statistic from sample to sample. Different samples yield different statistics randomly.
Natural variation in a statistic from sample to sample. Different samples yield different statistics randomly.
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Which term names random error that causes results to vary from sample to sample?
Which term names random error that causes results to vary from sample to sample?
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Variability. Unpredictable fluctuations, not systematic errors.
Variability. Unpredictable fluctuations, not systematic errors.
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What is the key purpose of random sampling in inference?
What is the key purpose of random sampling in inference?
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To reduce selection bias and support generalization to the population. Ensures sample represents population fairly.
To reduce selection bias and support generalization to the population. Ensures sample represents population fairly.
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What is a random sample?
What is a random sample?
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A sample selected by chance so each member has a known probability. Ensures representativeness through probabilistic selection.
A sample selected by chance so each member has a known probability. Ensures representativeness through probabilistic selection.
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Which phrase best describes statistical inference?
Which phrase best describes statistical inference?
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Using sample data to draw conclusions about population parameters. Sample statistics estimate unknown population parameters.
Using sample data to draw conclusions about population parameters. Sample statistics estimate unknown population parameters.
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What is the definition of a sample in statistical inference?
What is the definition of a sample in statistical inference?
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A subset of the population actually observed. Selected from the population to make inferences about the whole.
A subset of the population actually observed. Selected from the population to make inferences about the whole.
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What is the definition of a population in statistical inference?
What is the definition of a population in statistical inference?
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The entire group of individuals or measurements of interest. Includes all subjects being studied, not just those observed.
The entire group of individuals or measurements of interest. Includes all subjects being studied, not just those observed.
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What is the standard error?
What is the standard error?
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The standard deviation of a statistic’s sampling distribution. Measures typical variation of a statistic across samples.
The standard deviation of a statistic’s sampling distribution. Measures typical variation of a statistic across samples.
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What is the formula for the sample proportion if $x$ successes occur in $n$ trials?
What is the formula for the sample proportion if $x$ successes occur in $n$ trials?
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$\hat{p}=\frac{x}{n}$. Divide count of successes by total trials.
$\hat{p}=\frac{x}{n}$. Divide count of successes by total trials.
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What is the formula for the sample mean of values $x_1,\dots,x_n$?
What is the formula for the sample mean of values $x_1,\dots,x_n$?
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$\bar{x}=\frac{1}{n}\sum_{i=1}^{n} x_i$. Sum all values and divide by sample size.
$\bar{x}=\frac{1}{n}\sum_{i=1}^{n} x_i$. Sum all values and divide by sample size.
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What does the law of large numbers imply for the sample mean as $n$ increases?
What does the law of large numbers imply for the sample mean as $n$ increases?
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The sample mean tends to get closer to the population mean. Larger samples provide more accurate estimates.
The sample mean tends to get closer to the population mean. Larger samples provide more accurate estimates.
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Which term names a systematic error that shifts results away from the truth?
Which term names a systematic error that shifts results away from the truth?
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Bias. Consistently over- or underestimates the true parameter.
Bias. Consistently over- or underestimates the true parameter.
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Which statement is correct: (A) a parameter varies by sample, (B) a statistic varies by sample?
Which statement is correct: (A) a parameter varies by sample, (B) a statistic varies by sample?
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(B) a statistic varies by sample. Parameters are fixed; statistics change with samples.
(B) a statistic varies by sample. Parameters are fixed; statistics change with samples.
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Identify the main error: using a sample of volunteers to estimate a population mean.
Identify the main error: using a sample of volunteers to estimate a population mean.
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Selection bias (nonrandom sampling). Volunteers aren't randomly selected, causing bias.
Selection bias (nonrandom sampling). Volunteers aren't randomly selected, causing bias.
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Identify the population parameter estimated by $\bar{x}$.
Identify the population parameter estimated by $\bar{x}$.
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The population mean $\mu$. Sample mean estimates population mean.
The population mean $\mu$. Sample mean estimates population mean.
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What is the sampling distribution of a statistic?
What is the sampling distribution of a statistic?
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The distribution of that statistic over all possible random samples. Shows how a statistic behaves across repeated sampling.
The distribution of that statistic over all possible random samples. Shows how a statistic behaves across repeated sampling.
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Identify the population parameter estimated by $\hat{p}$.
Identify the population parameter estimated by $\hat{p}$.
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The population proportion $p$. Sample proportion estimates population proportion.
The population proportion $p$. Sample proportion estimates population proportion.
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Which option is a random sample: (A) volunteers online, (B) every $10^{\text{th}}$ customer from a random start?
Which option is a random sample: (A) volunteers online, (B) every $10^{\text{th}}$ customer from a random start?
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(B) every $10^{\text{th}}$ customer from a random start. Systematic sampling with random start gives equal chances.
(B) every $10^{\text{th}}$ customer from a random start. Systematic sampling with random start gives equal chances.
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Identify the key flaw for inference: sampling only volunteers from a population to estimate $p$.
Identify the key flaw for inference: sampling only volunteers from a population to estimate $p$.
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Voluntary response bias (not a random sample). Self-selection creates biased, non-representative samples.
Voluntary response bias (not a random sample). Self-selection creates biased, non-representative samples.
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What is the definition of a random sample from a population?
What is the definition of a random sample from a population?
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A sample selected by chance so each unit has a known probability. Random sampling ensures unbiased representation of the population.
A sample selected by chance so each unit has a known probability. Random sampling ensures unbiased representation of the population.
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What is the definition of a statistic in the context of sampling and inference?
What is the definition of a statistic in the context of sampling and inference?
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A numerical value computed from a sample. Statistics are calculated from sample data to estimate parameters.
A numerical value computed from a sample. Statistics are calculated from sample data to estimate parameters.
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What is the definition of a population parameter in statistical inference?
What is the definition of a population parameter in statistical inference?
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A numerical value describing a population (often unknown). Parameters are fixed but unknown characteristics we want to estimate.
A numerical value describing a population (often unknown). Parameters are fixed but unknown characteristics we want to estimate.
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Which inference goal matches $\hat{p}$: estimating a population mean or a population proportion?
Which inference goal matches $\hat{p}$: estimating a population mean or a population proportion?
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Estimating a population proportion $p$. $\hat{p}$ is the sample proportion, used to estimate population proportion $p$.
Estimating a population proportion $p$. $\hat{p}$ is the sample proportion, used to estimate population proportion $p$.
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What is the definition of sampling variability?
What is the definition of sampling variability?
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Natural variation in a statistic from sample to sample. Different samples yield different statistics due to randomness.
Natural variation in a statistic from sample to sample. Different samples yield different statistics due to randomness.
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What is the main purpose of using a random sample when making inferences about a population?
What is the main purpose of using a random sample when making inferences about a population?
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To reduce bias and support generalization to the population. Random sampling prevents systematic errors in estimation.
To reduce bias and support generalization to the population. Random sampling prevents systematic errors in estimation.
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What is the definition of bias in the context of sampling and inference?
What is the definition of bias in the context of sampling and inference?
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A systematic tendency for a statistic to miss the true parameter. Bias causes consistent over- or underestimation of the parameter.
A systematic tendency for a statistic to miss the true parameter. Bias causes consistent over- or underestimation of the parameter.
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